Jia-Bao Ji, Zhaoheng Guo, Taran Driver, Cynthia S. Trevisan, David Cesar, Xinxin Cheng, Joseph Duris, Paris L. Franz, James Glownia, Xiaochun Gong, Daniel Hammerland, Meng Han, Saijoscha Heck, Matthias Hoffmann, Andrei Kamalov, Kirk A. Larsen, Xiang Li, Ming-Fu Lin, Yuchen Liu, C. William McCurdy, Razib Obaid, Jordan T. O’Neal, Thomas N. Rescigno, River R. Robles, Nicholas Sudar, Peter Walter, Anna L. Wang, Jun Wang, Thomas J. A. Wolf, Zhen Zhang, Kiyoshi Ueda, Robert R. Lucchese, Agostino Marinelli, James P. Cryan, Hans Jakob Wörner
Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, the spectral congestion of valence photoelectron spectra sets fundamental limits to the complexity of systems that can be studied, and the delocalization of valence electron wave functions blurs the spatial origin of the photoelectron wave packet. Using attosecond x-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: The photoelectron spectra remain atomlike, the measurements become element specific, and the observed scattering dynamics originate from a pointlike source when multicenter interference effects are negligible. We exploit these unique features to reveal the effects of changing functional groups (C-H vs N) and symmetry on attosecond scattering dynamics by measuring and calculating the photoionization delays between N − 1 s and C−1s core shells of a series of aromatic azabenzene molecules. Remarkably, the delays increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wave function with the replacement of C-H groups by N atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unraveling attosecond electron dynamics in complex matter.
阿秒光发射或光电离延迟是对物质结构和电子动力学的独特探测。然而，价电子能谱的频谱拥挤性对可研究系统的复杂性设置了基本限制，价电子波函数的离域模糊了光电子波包的空间起源。利用来自LCLS的阿秒x射线脉冲，我们证明了测量核心级延迟的关键优势：光电子能谱保持原子状，测量变得特定于元素，并且当多中心干涉效应可以忽略不计时，观察到的散射动力学源于点状源。我们利用这些独特的特征，通过测量和计算一系列芳香氮杂苯分子的N−1 s和C−1 s核壳之间的光离延迟，揭示了官能团（C- h vs N）和对称性变化对阿秒散射动力学的影响。值得注意的是，延迟随着分子中氮原子数量的增加而增加，并显示出多重共振。我们发现了两个先前未知的调节相关阿秒动力学的机制，即随着C-H基团被N原子取代，捕获波函数的约束增强，和光发射的部分波之间的耦合强度随着对称性的增加而降低。这项研究展示了通过测量核心能级的光电离延迟来揭示复杂物质中阿秒电子动力学的独特机会。
{"title":"Attosecond X-Ray Core-Level Chronoscopy of Aromatic Molecules","authors":"Jia-Bao Ji, Zhaoheng Guo, Taran Driver, Cynthia S. Trevisan, David Cesar, Xinxin Cheng, Joseph Duris, Paris L. Franz, James Glownia, Xiaochun Gong, Daniel Hammerland, Meng Han, Saijoscha Heck, Matthias Hoffmann, Andrei Kamalov, Kirk A. Larsen, Xiang Li, Ming-Fu Lin, Yuchen Liu, C. William McCurdy, Razib Obaid, Jordan T. O’Neal, Thomas N. Rescigno, River R. Robles, Nicholas Sudar, Peter Walter, Anna L. Wang, Jun Wang, Thomas J. A. Wolf, Zhen Zhang, Kiyoshi Ueda, Robert R. Lucchese, Agostino Marinelli, James P. Cryan, Hans Jakob Wörner","doi":"10.1103/dp5w-qxqc","DOIUrl":"https://doi.org/10.1103/dp5w-qxqc","url":null,"abstract":"Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, the spectral congestion of valence photoelectron spectra sets fundamental limits to the complexity of systems that can be studied, and the delocalization of valence electron wave functions blurs the spatial origin of the photoelectron wave packet. Using attosecond x-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: The photoelectron spectra remain atomlike, the measurements become element specific, and the observed scattering dynamics originate from a pointlike source when multicenter interference effects are negligible. We exploit these unique features to reveal the effects of changing functional groups (C-H vs N) and symmetry on attosecond scattering dynamics by measuring and calculating the photoionization delays between N</a:mi> −</a:mtext> 1</a:mn> s</a:mi> </a:mrow> </a:math> and <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <d:mrow> <d:mi mathvariant=\"normal\">C</d:mi> <d:mtext>−</d:mtext> <d:mn>1</d:mn> <d:mi>s</d:mi> </d:mrow> </d:math> core shells of a series of aromatic azabenzene molecules. Remarkably, the delays increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wave function with the replacement of C-H groups by N atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unraveling attosecond electron dynamics in complex matter.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"27 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145515965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Di Tian, Haotian Zheng, Zewei Huang, Sijie Wu, Pengcheng Li, Cong Li, Jianbing Zhang, Xinyu Shu, Jinling Zhou, Yang Liu, Yanhong Gu, Meng Wang, Di Yi, Tianxiang Nan, Zhen Chen, Qing He, Huaqiang Wu, Shuyun Zhou, Weidong Luo, Pu Yu
Layered oxide materials, with their two-dimensional crystalline architectures and tunable interlayer interaction, serve as a fertile field for harnessing emergent quantum phenomena. Among these materials, metallic delafossites (e.g., PdCoO 2 ) have emerged as a prominent system with extraordinary two-dimensional electronic properties, though their intrinsic lack of ferromagnetism has remained a fundamental constraint. Here, we report the creation of robust, bulk high-temperature ferromagnetism ( Tc>420K ) in inherently nonmagnetic PdCoO2 through controlled hydrogenation while preserving the delafossite structure. This process induces layer-selective electron doping into CoO2 layers, stabilizing Ising-type ferromagnetism with pronounced perpendicular magnetic anisotropy while preserving the material’s exceptional metallicity. Remarkably, the system self-assembles into a superlattice of alternating metallic Pd and insulating ferromagnetic hydrogenated CoO2 layers, enabling an unconventional anomalous Hall effect mediated by interlayer spin-charge coupling. These findings demonstrate that bulk ferromagnetism can be achieved in delafossite oxides while preserving their structural integrity, positioning hydrogenated delafossites as a versatile platform for exploring correlated quantum effects and designing multifunctional devices.
{"title":"Hydrogenated PdCoO 2 : A layered Metallic Oxide with Robust Room-Temperature Ferromagnetism","authors":"Di Tian, Haotian Zheng, Zewei Huang, Sijie Wu, Pengcheng Li, Cong Li, Jianbing Zhang, Xinyu Shu, Jinling Zhou, Yang Liu, Yanhong Gu, Meng Wang, Di Yi, Tianxiang Nan, Zhen Chen, Qing He, Huaqiang Wu, Shuyun Zhou, Weidong Luo, Pu Yu","doi":"10.1103/3mgc-z9wv","DOIUrl":"https://doi.org/10.1103/3mgc-z9wv","url":null,"abstract":"Layered oxide materials, with their two-dimensional crystalline architectures and tunable interlayer interaction, serve as a fertile field for harnessing emergent quantum phenomena. Among these materials, metallic delafossites (e.g., PdCoO</a:mi> 2</a:mn> </a:msub> </a:mrow> </a:math> ) have emerged as a prominent system with extraordinary two-dimensional electronic properties, though their intrinsic lack of ferromagnetism has remained a fundamental constraint. Here, we report the creation of robust, bulk high-temperature ferromagnetism ( <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <c:mrow> <c:msub> <c:mi>T</c:mi> <c:mi>c</c:mi> </c:msub> <c:mo>></c:mo> <c:mn>420</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi mathvariant=\"normal\">K</c:mi> </c:mrow> </c:math> ) in inherently nonmagnetic <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <f:mrow> <f:msub> <f:mi>PdCoO</f:mi> <f:mn>2</f:mn> </f:msub> </f:mrow> </f:math> through controlled hydrogenation while preserving the delafossite structure. This process induces layer-selective electron doping into <h:math xmlns:h=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <h:mrow> <h:msub> <h:mi>CoO</h:mi> <h:mn>2</h:mn> </h:msub> </h:mrow> </h:math> layers, stabilizing Ising-type ferromagnetism with pronounced perpendicular magnetic anisotropy while preserving the material’s exceptional metallicity. Remarkably, the system self-assembles into a superlattice of alternating metallic Pd and insulating ferromagnetic hydrogenated <j:math xmlns:j=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <j:mrow> <j:msub> <j:mi>CoO</j:mi> <j:mn>2</j:mn> </j:msub> </j:mrow> </j:math> layers, enabling an unconventional anomalous Hall effect mediated by interlayer spin-charge coupling. These findings demonstrate that bulk ferromagnetism can be achieved in delafossite oxides while preserving their structural integrity, positioning hydrogenated delafossites as a versatile platform for exploring correlated quantum effects and designing multifunctional devices.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"144 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145515966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite “resources” are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as τ C ϵ τ ≥ 1 − η . This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error. The generalization to general quantum dynamics involving a system coupled to a finite bath implies that the dissipative cost becomes infinite as the quantum system is exactly cooled down to the ground state or perfectly reset to a pure state, thereby resolving an open question regarding the thermodynamic cost of information erasure.
阐明物理系统固有的基本限制是物理学的中心课题。对于重要的热力学操作，如信息擦除、冷却和复制，必须花费时间和精力成本等资源，才能在预定的误差范围内达到预期的结果。在冷却的背景下，热力学第三定律的不可达性原理断言，需要无限的“资源”才能达到绝对零度。然而，在随机和量子热力学的框架内，相关资源的精确识别以及它们如何共同约束可实现的误差仍然不清楚。在这项工作中，我们引入了分离状态的概念，其中包括完全未占用状态和已占用状态，并制定了相应的热力学成本和误差，从而为广泛的热力学操作建立了一个统一的框架。然后，我们揭示了旨在创建分离状态的热力学操作的时间、成本和误差之间的三向权衡关系，简单地表示为τ C ε τ≥1−η。这一基本关系适用于各种热力学操作，包括信息擦除、冷却和复制。它以一般形式对热力学第三定律中的不可达性原理进行了深刻的量化。在这种关系的基础上，我们探讨了控制冷却操作的定量限制，分离状态的制备，以及精确经典复制的不去定理。此外，我们将这些发现扩展到量子状态，包括马尔可夫和非马尔可夫动力学。具体来说，在Lindblad动力学中，我们导出了一个类似的三方权衡关系，量化了在给定误差下达到纯状态的成本。一般量子动力学的推广涉及到一个系统耦合到一个有限的槽意味着耗散成本变得无限，当量子系统完全冷却到基态或完全重置到纯态，从而解决了一个关于信息擦除的热力学成本的开放问题。
{"title":"Time-Cost-Error Trade-Off Relation in Thermodynamics: The Third Law and Beyond","authors":"Tan Van Vu, Keiji Saito","doi":"10.1103/l6b9-rg1j","DOIUrl":"https://doi.org/10.1103/l6b9-rg1j","url":null,"abstract":"Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite “resources” are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as τ</a:mi> C</a:mi> ϵ</a:mi> </a:mrow> τ</a:mi> </a:mrow> </a:msub> ≥</a:mo> 1</a:mn> −</a:mo> η</a:mi> </a:mrow> </a:math> . This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error. The generalization to general quantum dynamics involving a system coupled to a finite bath implies that the dissipative cost becomes infinite as the quantum system is exactly cooled down to the ground state or perfectly reset to a pure state, thereby resolving an open question regarding the thermodynamic cost of information erasure.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"1 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145498174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jonathan Bauermann, Giacomo Bartolucci, Job Boekhoven, Frank Jülicher, Christoph A. Weber
Most emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a nonequilibrium steady state with monodisperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a supercritical transition controlled by the conserved quantity between two classes of chemically active droplets: intensive and extensive active droplets. While intensive droplets reach a stationary size mainly controlled by the interplay between reactions and diffusion, the size of an extensive active droplet scales with the system size. For intensive droplets, growth arrests at a finite size. Thus, they can be far apart from each other and evolve independently from other droplets in an active emulsion. The growth of extensive droplets, however, arrests due to the presence of other droplets in the emulsion. In both cases, monodisperse emulsions can emerge. We show how the supercritical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions.
{"title":"Critical Transition between Intensive and Extensive Active Droplets","authors":"Jonathan Bauermann, Giacomo Bartolucci, Job Boekhoven, Frank Jülicher, Christoph A. Weber","doi":"10.1103/4nnd-tdky","DOIUrl":"https://doi.org/10.1103/4nnd-tdky","url":null,"abstract":"Most emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a nonequilibrium steady state with monodisperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a supercritical transition controlled by the conserved quantity between two classes of chemically active droplets: intensive and extensive active droplets. While intensive droplets reach a stationary size mainly controlled by the interplay between reactions and diffusion, the size of an extensive active droplet scales with the system size. For intensive droplets, growth arrests at a finite size. Thus, they can be far apart from each other and evolve independently from other droplets in an active emulsion. The growth of extensive droplets, however, arrests due to the presence of other droplets in the emulsion. In both cases, monodisperse emulsions can emerge. We show how the supercritical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"262 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145498611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sebastian Buchberger, Yann in ’t Veld, Akhil Rajan, Philip A. E. Murgatroyd, Brendan Edwards, Bruno K. Saika, Naina Kushwaha, Maria H. Visscher, Jan Berges, Dina Carbone, Jacek Osiecki, Craig Polley, Tim Wehling, Phil D. C. King
TiSe 2 has long been considered one of the best candidate materials to host the elusive excitonic insulator (EI) phase. However, a finite coupling to the lattice can generically be expected, while a lack of “smoking-gun” signatures for the importance of the electron-hole interaction in driving the phase transition has rendered it challenging to distinguish the EI from the conventional charge-density wave (CDW) phase. Here, we demonstrate a new approach, exploiting the susceptibility of excitons to dielectric screening. We combine mechanical exfoliation with molecular-beam epitaxy to fabricate ultraclean van der Waals heterostructures of monolayer (ML) TiSe2 /graphite and ML TiSe2/h -BN. We observe how the modified substrate screening environment drives a renormalization of the quasiparticle band gap of the TiSe2 layer, signifying its susceptibility to Coulomb engineering. The temperature-dependent evolution of its electronic structure, however, remains unaffected, indicating that excitons are not required to drive the CDW transition in TiSe2 .
tis2一直被认为是承载难以捉摸的激子绝缘体（EI）相的最佳候选材料之一。然而，与晶格的有限耦合通常是可以预期的，而缺乏电子-空穴相互作用在驱动相变中的重要性的“确凿”特征，使得将EI与传统的电荷密度波（CDW）相区分开来具有挑战性。在这里，我们展示了一种新的方法，利用激子对介电屏蔽的敏感性。我们将机械剥离与分子束外延相结合，制备了单层（ML） tis2 /石墨和ML tis2 / h -BN的超净范德华异质结构。我们观察到改进的衬底筛选环境如何驱动ties2层准粒子带隙的重整化，表明其对库仑工程的敏感性。然而，其电子结构的温度依赖演化仍然不受影响，这表明激子不需要驱动ties2中的CDW转变。
{"title":"Persistence of Charge Ordering Instability to Coulomb Engineering in the Excitonic Insulator Candidate TiSe 2 ","authors":"Sebastian Buchberger, Yann in ’t Veld, Akhil Rajan, Philip A. E. Murgatroyd, Brendan Edwards, Bruno K. Saika, Naina Kushwaha, Maria H. Visscher, Jan Berges, Dina Carbone, Jacek Osiecki, Craig Polley, Tim Wehling, Phil D. C. King","doi":"10.1103/9trc-9865","DOIUrl":"https://doi.org/10.1103/9trc-9865","url":null,"abstract":"TiSe</a:mi> 2</a:mn> </a:msub> </a:math> has long been considered one of the best candidate materials to host the elusive excitonic insulator (EI) phase. However, a finite coupling to the lattice can generically be expected, while a lack of “smoking-gun” signatures for the importance of the electron-hole interaction in driving the phase transition has rendered it challenging to distinguish the EI from the conventional charge-density wave (CDW) phase. Here, we demonstrate a new approach, exploiting the susceptibility of excitons to dielectric screening. We combine mechanical exfoliation with molecular-beam epitaxy to fabricate ultraclean van der Waals heterostructures of monolayer (ML) <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <c:mrow> <c:msub> <c:mrow> <c:mi>TiSe</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msub> </c:mrow> </c:math> /graphite and ML <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <e:mrow> <e:msub> <e:mrow> <e:mi>TiSe</e:mi> </e:mrow> <e:mrow> <e:mn>2</e:mn> </e:mrow> </e:msub> </e:mrow> <e:mo>/</e:mo> <e:mi>h</e:mi> </e:math> -BN. We observe how the modified substrate screening environment drives a renormalization of the quasiparticle band gap of the <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <g:mrow> <g:msub> <g:mrow> <g:mi>TiSe</g:mi> </g:mrow> <g:mrow> <g:mn>2</g:mn> </g:mrow> </g:msub> </g:mrow> </g:math> layer, signifying its susceptibility to Coulomb engineering. The temperature-dependent evolution of its electronic structure, however, remains unaffected, indicating that excitons are not required to drive the CDW transition in <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <i:mrow> <i:msub> <i:mrow> <i:mi>TiSe</i:mi> </i:mrow> <i:mrow> <i:mn>2</i:mn> </i:mrow> </i:msub> </i:mrow> </i:math> .","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"1 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145492381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yijia Xu, Yixu Wang, Christophe Vuillot, Victor V. Albert
Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode’s occupation number modulo two, but this can be relaxed to a linear occupation-number constraint using the alternative two-mode pair-cat encoding. We construct multimode codes with similar linear constraints using any two integer matrices satisfying a Calderbank-Shor-Steane-like homological condition of a quantum rotor code. Just like the pair-cat code, syndrome extraction can be performed in tandem with stabilizing dissipation using current superconducting-circuit designs. The framework includes codes with various finite- or infinite-dimensional code spaces and codes with finite or infinite Fock-state support. It encompasses two-component cat, pair-cat, dual-rail, two-mode binomial, various bosonic repetition codes, and aspects of χ -squared encodings, while also yielding codes from homological products, lattices, generalized coherent states, and algebraic varieties. Among our examples are analogs of repetition codes, the Shor code, and a surface-code-like construction that is not a concatenation of a known cat code with the qubit surface code. Code words are coherent states projected into a Fock-state subspace defined by an integer matrix, and their overlaps are governed by Gelfand-Kapranov-Zelevinsky hypergeometric functions.
{"title":"Letting the Tiger out of Its Cage: Bosonic Coding without Concatenation","authors":"Yijia Xu, Yixu Wang, Christophe Vuillot, Victor V. Albert","doi":"10.1103/ls5r-vj7r","DOIUrl":"https://doi.org/10.1103/ls5r-vj7r","url":null,"abstract":"Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode’s occupation number modulo two, but this can be relaxed to a linear occupation-number constraint using the alternative two-mode pair-cat encoding. We construct multimode codes with similar linear constraints using any two integer matrices satisfying a Calderbank-Shor-Steane-like homological condition of a quantum rotor code. Just like the pair-cat code, syndrome extraction can be performed in tandem with stabilizing dissipation using current superconducting-circuit designs. The framework includes codes with various finite- or infinite-dimensional code spaces and codes with finite or infinite Fock-state support. It encompasses two-component cat, pair-cat, dual-rail, two-mode binomial, various bosonic repetition codes, and aspects of χ</a:mi> </a:math> -squared encodings, while also yielding codes from homological products, lattices, generalized coherent states, and algebraic varieties. Among our examples are analogs of repetition codes, the Shor code, and a surface-code-like construction that is not a concatenation of a known cat code with the qubit surface code. Code words are coherent states projected into a Fock-state subspace defined by an integer matrix, and their overlaps are governed by Gelfand-Kapranov-Zelevinsky hypergeometric functions.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"29 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145478059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited. GNNs can encounter difficulties in gathering information from nodes that are far apart by iterated aggregation steps. This situation is partly caused by so-called oversmoothing; and overcoming it is one of the practically motivated challenges. We consider the situation where information is aggregated by multiple steps of convolution, leading to graph convolutional networks (GCNs). We analyze the generalization performance of a basic GCN, trained for node classification on data generated by the contextual stochastic block model. We predict its asymptotic performance by deriving the free energy of the problem, using the replica method, in the high-dimensional limit. Calling the number of convolutional steps, we show the importance of going to large depth to approach the Bayes optimality. We detail how the architecture of the GCN has to scale with the depth to avoid oversmoothing. The resulting large depth limit can be close to the Bayes optimality and leads to a continuous GCN. Technically, we tackle this continuous limit via an approach that resembles dynamical mean-field theory with constraints at the initial and final times. An expansion around large regularization allows us to solve the corresponding equations for the performance of the deep GCN. This promising tool may contribute to the analysis of further deep neural networks.
{"title":"Statistical Physics Analysis of Graph Neural Networks: Approaching Optimality in the Contextual Stochastic Block Model","authors":"O. Duranthon, L. Zdeborová","doi":"10.1103/lfxj-hbsk","DOIUrl":"https://doi.org/10.1103/lfxj-hbsk","url":null,"abstract":"Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited. GNNs can encounter difficulties in gathering information from nodes that are far apart by iterated aggregation steps. This situation is partly caused by so-called oversmoothing; and overcoming it is one of the practically motivated challenges. We consider the situation where information is aggregated by multiple steps of convolution, leading to graph convolutional networks (GCNs). We analyze the generalization performance of a basic GCN, trained for node classification on data generated by the contextual stochastic block model. We predict its asymptotic performance by deriving the free energy of the problem, using the replica method, in the high-dimensional limit. Calling the number of convolutional steps, we show the importance of going to large depth to approach the Bayes optimality. We detail how the architecture of the GCN has to scale with the depth to avoid oversmoothing. The resulting large depth limit can be close to the Bayes optimality and leads to a continuous GCN. Technically, we tackle this continuous limit via an approach that resembles dynamical mean-field theory with constraints at the initial and final times. An expansion around large regularization allows us to solve the corresponding equations for the performance of the deep GCN. This promising tool may contribute to the analysis of further deep neural networks.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"142 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145484745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea De Luca, Chunxiao Liu, Adam Nahum, Tianci Zhou
We consider the universal aspects of two problems: (i) the singular value structure of a product M t = m t m t − 1 … m 1 of many large independent random matrices and (ii) the slow purification of a large number of qubits by repeated quantum measurements. The time-evolution operator in the latter case is again a product of matrices mi , representing time steps in the evolution, but the mi are now nontrivially correlated as a result of Born’s rule. Both processes are associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification and that (i) and (ii) represent distinct “universality classes” with distinct scaling functions. Using the replica trick, these universality classes correspond to effective one-dimensional statistical mechanics models for a gas of “kinks,” representing domain walls between elements of the permutation group. This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks. These results apply to longtime purification in spatially local monitored circuit models on the entangled side of the measurement phase transition.
我们考虑两个问题的普遍方面：(i)许多大型独立随机矩阵的乘积M t = M t M t - 1…M 1的奇异值结构和（ii）通过重复量子测量对大量量子位的缓慢纯化。后一种情况下的时间演化算子又是矩阵mi的乘积，表示演化过程中的时间步长，但由于玻恩法则，现在这些mi是非平凡相关的。这两个过程都与熵的自然度量作为时间的函数或乘积中矩阵数的函数的衰减有关。我们认为，对于一个广泛的模型类，每个过程都是用净化的通用标度形式来描述的，并且(i)和（ii）表示具有不同标度函数的不同的“通用性类”。使用复制技巧，这些普遍性类对应于“扭结”气体的有效一维统计力学模型，表示置换群元素之间的域壁。这是随机电路和张量网络有效统计力学模型的一个具有指导意义的低维极限。这些结果适用于在测量相变纠缠侧的空间局部监测电路模型中的长期净化。
{"title":"Universality Classes for Purification in Nonunitary Quantum Processes","authors":"Andrea De Luca, Chunxiao Liu, Adam Nahum, Tianci Zhou","doi":"10.1103/wlj6-mkk4","DOIUrl":"https://doi.org/10.1103/wlj6-mkk4","url":null,"abstract":"We consider the universal aspects of two problems: (i) the singular value structure of a product M</a:mi> t</a:mi> </a:msub> =</a:mo> m</a:mi> t</a:mi> </a:msub> m</a:mi> t</a:mi> −</a:mo> 1</a:mn> </a:mrow> </a:msub> …</a:mo> m</a:mi> 1</a:mn> </a:msub> </a:math> of many large independent random matrices and (ii) the slow purification of a large number of qubits by repeated quantum measurements. The time-evolution operator in the latter case is again a product of matrices <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <c:msub> <c:mi>m</c:mi> <c:mi>i</c:mi> </c:msub> </c:math> , representing time steps in the evolution, but the <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <e:msub> <e:mi>m</e:mi> <e:mi>i</e:mi> </e:msub> </e:math> are now nontrivially correlated as a result of Born’s rule. Both processes are associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification and that (i) and (ii) represent distinct “universality classes” with distinct scaling functions. Using the replica trick, these universality classes correspond to effective one-dimensional statistical mechanics models for a gas of “kinks,” representing domain walls between elements of the permutation group. This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks. These results apply to longtime purification in spatially local monitored circuit models on the entangled side of the measurement phase transition.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"43 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory, and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant time slice in a flat spacetime. Our prescription starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes, in general, a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and we show that it leads to results with self-consistent physical properties of temporal entanglement.
{"title":"Temporal Entanglement from Holographic Entanglement Entropy","authors":"Michal P. Heller, Fabio Ori, Alexandre Serantes","doi":"10.1103/qlsv-gp22","DOIUrl":"https://doi.org/10.1103/qlsv-gp22","url":null,"abstract":"Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory, and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant time slice in a flat spacetime. Our prescription starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes, in general, a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and we show that it leads to results with self-consistent physical properties of temporal entanglement.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"93 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145455643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Valentini, M. W. van Mourik, F. Butt, J. Wahl, M. Dietl, M. Pfeifer, F. Anmasser, Y. Colombe, C. Rössler, P. C. Holz, R. Blatt, A. Bermudez, M. Müller, T. Monz, P. Schindler
A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the quantum spring array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.
{"title":"Demonstration of Two-Dimensional Connectivity for a Scalable Error-Corrected Ion-Trap Quantum Processor Architecture","authors":"M. Valentini, M. W. van Mourik, F. Butt, J. Wahl, M. Dietl, M. Pfeifer, F. Anmasser, Y. Colombe, C. Rössler, P. C. Holz, R. Blatt, A. Bermudez, M. Müller, T. Monz, P. Schindler","doi":"10.1103/b9s1-6r44","DOIUrl":"https://doi.org/10.1103/b9s1-6r44","url":null,"abstract":"A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the quantum spring array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"97 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145455644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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