Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasi-periodically coupled to each other. The spin chains are incommensurate and are coupled through a short range exchange interaction of the $XXZ$ type that decays exponentially with the distance. Using exact diagonalization, matrix product states and density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a pre-thermal phase whose entanglement entropy grows logarithmically with time.
{"title":"Disorder free many-body localization transition in two quasiperiodically coupled Heisenberg spin chains","authors":"K. G. S. H. Gunawardana, Bruno Uchoa","doi":"arxiv-2405.04516","DOIUrl":"https://doi.org/arxiv-2405.04516","url":null,"abstract":"Disorder free many-body localization (MBL) can occur in interacting systems\u0000that can dynamically generate their own disorder. We address the thermal-MBL\u0000phase transition of two isotropic Heisenberg spin chains that are\u0000quasi-periodically coupled to each other. The spin chains are incommensurate\u0000and are coupled through a short range exchange interaction of the $XXZ$ type\u0000that decays exponentially with the distance. Using exact diagonalization,\u0000matrix product states and density matrix renormalization group, we calculate\u0000the time evolution of the entanglement entropy at long times and extract the\u0000inverse participation ratio in the thermodynamic limit. We show that this\u0000system has a robust MBL phase. We establish the phase diagram with the onset of\u0000MBL as a function of the interchain exchange coupling and of the\u0000incommensuration between the spin chains. The Ising limit of the interchain\u0000interaction optimizes the stability of the MBL phase over a broad range of\u0000incommensurations above a given critical exchange coupling. Incorporation of\u0000interchain spin flips significantly enhances entanglement between the spin\u0000chains and produces delocalization, favoring a pre-thermal phase whose\u0000entanglement entropy grows logarithmically with time.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
David van Driel, Rouven Koch, Vincent P. M. Sietses, Sebastiaan L. D. ten Haaf, Chun-Xiao Liu, Francesco Zatelli, Bart Roovers, Alberto Bordin, Nick van Loo, Guanzhong Wang, Jan Cornelis Wolff, Grzegorz P. Mazur, Tom Dvir, Ivan Kulesh, Qingzhen Wang, A. Mert Bozkurt, Sasa Gazibegovic, Ghada Badawy, Erik P. A. M. Bakkers, Michael Wimmer, Srijit Goswami, Jose L. Lado, Leo P. Kouwenhoven, Eliska Greplova
Contemporary quantum devices are reaching new limits in size and complexity, allowing for the experimental exploration of emergent quantum modes. However, this increased complexity introduces significant challenges in device tuning and control. Here, we demonstrate autonomous tuning of emergent Majorana zero modes in a minimal realization of a Kitaev chain. We achieve this task using cross-platform transfer learning. First, we train a tuning model on a theory model. Next, we retrain it using a Kitaev chain realization in a two-dimensional electron gas. Finally, we apply this model to tune a Kitaev chain realized in quantum dots coupled through a semiconductor-superconductor section in a one-dimensional nanowire. Utilizing a convolutional neural network, we predict the tunneling and Cooper pair splitting rates from differential conductance measurements, employing these predictions to adjust the electrochemical potential to a Majorana sweet spot. The algorithm successfully converges to the immediate vicinity of a sweet spot (within 1.5 mV in 67.6% of attempts and within 4.5 mV in 80.9% of cases), typically finding a sweet spot in 45 minutes or less. This advancement is a stepping stone towards autonomous tuning of emergent modes in interacting systems, and towards foundational tuning machine learning models that can be deployed across a range of experimental platforms.
{"title":"Cross-Platform Autonomous Control of Minimal Kitaev Chains","authors":"David van Driel, Rouven Koch, Vincent P. M. Sietses, Sebastiaan L. D. ten Haaf, Chun-Xiao Liu, Francesco Zatelli, Bart Roovers, Alberto Bordin, Nick van Loo, Guanzhong Wang, Jan Cornelis Wolff, Grzegorz P. Mazur, Tom Dvir, Ivan Kulesh, Qingzhen Wang, A. Mert Bozkurt, Sasa Gazibegovic, Ghada Badawy, Erik P. A. M. Bakkers, Michael Wimmer, Srijit Goswami, Jose L. Lado, Leo P. Kouwenhoven, Eliska Greplova","doi":"arxiv-2405.04596","DOIUrl":"https://doi.org/arxiv-2405.04596","url":null,"abstract":"Contemporary quantum devices are reaching new limits in size and complexity,\u0000allowing for the experimental exploration of emergent quantum modes. However,\u0000this increased complexity introduces significant challenges in device tuning\u0000and control. Here, we demonstrate autonomous tuning of emergent Majorana zero\u0000modes in a minimal realization of a Kitaev chain. We achieve this task using\u0000cross-platform transfer learning. First, we train a tuning model on a theory\u0000model. Next, we retrain it using a Kitaev chain realization in a\u0000two-dimensional electron gas. Finally, we apply this model to tune a Kitaev\u0000chain realized in quantum dots coupled through a semiconductor-superconductor\u0000section in a one-dimensional nanowire. Utilizing a convolutional neural\u0000network, we predict the tunneling and Cooper pair splitting rates from\u0000differential conductance measurements, employing these predictions to adjust\u0000the electrochemical potential to a Majorana sweet spot. The algorithm\u0000successfully converges to the immediate vicinity of a sweet spot (within 1.5 mV\u0000in 67.6% of attempts and within 4.5 mV in 80.9% of cases), typically finding a\u0000sweet spot in 45 minutes or less. This advancement is a stepping stone towards\u0000autonomous tuning of emergent modes in interacting systems, and towards\u0000foundational tuning machine learning models that can be deployed across a range\u0000of experimental platforms.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"324 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Sherrington-Kirkpatrick (SK) model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.
{"title":"Quenches in the Sherrington-Kirkpatrick model","authors":"Vittorio Erba, Freya Behrens, Florent Krzakala, Lenka Zdeborová","doi":"arxiv-2405.04267","DOIUrl":"https://doi.org/arxiv-2405.04267","url":null,"abstract":"The Sherrington-Kirkpatrick (SK) model is a prototype of a complex non-convex\u0000energy landscape. Dynamical processes evolving on such landscapes and locally\u0000aiming to reach minima are generally poorly understood. Here, we study\u0000quenches, i.e. dynamics that locally aim to decrease energy. We analyse the\u0000energy at convergence for two distinct algorithmic classes, single-spin flip\u0000and synchronous dynamics, focusing on greedy and reluctant strategies. We\u0000provide precise numerical analysis of the finite size effects and conclude\u0000that, perhaps counter-intuitively, the reluctant algorithm is compatible with\u0000converging to the ground state energy density, while the greedy strategy is\u0000not. Inspired by the single-spin reluctant and greedy algorithms, we\u0000investigate two synchronous time algorithms, the sync-greedy and sync-reluctant\u0000algorithms. These synchronous processes can be analysed using dynamical mean\u0000field theory (DMFT), and a new backtracking version of DMFT. Notably, this is\u0000the first time the backtracking DMFT is applied to study dynamical convergence\u0000properties in fully connected disordered models. The analysis suggests that the\u0000sync-greedy algorithm can also achieve energies compatible with the ground\u0000state, and that it undergoes a dynamical phase transition.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For Ising models with complex energy landscapes, whether the ground state can be found by neural networks depends heavily on the Hamming distance between the training datasets and the ground state. Despite the fact that various recently proposed generative models have shown good performance in solving Ising models, there is no adequate discussion on how to quantify their generalization capabilities. Here we design a Hamming distance regularizer in the framework of a class of generative models, variational autoregressive networks (VAN), to quantify the generalization capabilities of various network architectures combined with VAN. The regularizer can control the size of the overlaps between the ground state and the training datasets generated by networks, which, together with the success rates of finding the ground state, form a quantitative metric to quantify their generalization capabilities. We conduct numerical experiments on several prototypical network architectures combined with VAN, including feed-forward neural networks, recurrent neural networks, and graph neural networks, to quantify their generalization capabilities when solving Ising models. Moreover, considering the fact that the quantification of the generalization capabilities of networks on small-scale problems can be used to predict their relative performance on large-scale problems, our method is of great significance for assisting in the Neural Architecture Search field of searching for the optimal network architectures when solving large-scale Ising models.
对于具有复杂能谱的伊辛模型，神经网络能否找到基态在很大程度上取决于训练数据集与基态之间的汉明距离。尽管最近提出的各种生成模型在求解伊辛模型时表现出了良好的性能，但如何量化它们的泛化能力还没有充分的讨论。在此，我们在一类生成模型--变异自回归网络（VAN）的框架内设计了一个汉明距离正则器，以量化与 VAN 结合的各种网络架构的泛化能力。正则化器可以控制地面状态与网络生成的训练数据集之间的重叠大小，这与找到地面状态的成功率一起构成了量化网络泛化能力的量化指标。我们对几种与 VAN 结合的原型网络架构（包括前馈神经网络、递归神经网络和图神经网络）进行了数值实验，以量化它们在求解伊辛模型时的泛化能力。此外，考虑到量化网络在小规模问题上的泛化能力可以用来预测它们在大规模问题上的相对性能，我们的方法对于帮助神经架构搜索领域在求解大规模 Ising 模型时寻找最优网络架构具有重要意义。
{"title":"A method for quantifying the generalization capabilities of generative models for solving Ising models","authors":"Qunlong Ma, Zhi Ma, Ming Gao","doi":"arxiv-2405.03435","DOIUrl":"https://doi.org/arxiv-2405.03435","url":null,"abstract":"For Ising models with complex energy landscapes, whether the ground state can\u0000be found by neural networks depends heavily on the Hamming distance between the\u0000training datasets and the ground state. Despite the fact that various recently\u0000proposed generative models have shown good performance in solving Ising models,\u0000there is no adequate discussion on how to quantify their generalization\u0000capabilities. Here we design a Hamming distance regularizer in the framework of\u0000a class of generative models, variational autoregressive networks (VAN), to\u0000quantify the generalization capabilities of various network architectures\u0000combined with VAN. The regularizer can control the size of the overlaps between\u0000the ground state and the training datasets generated by networks, which,\u0000together with the success rates of finding the ground state, form a\u0000quantitative metric to quantify their generalization capabilities. We conduct\u0000numerical experiments on several prototypical network architectures combined\u0000with VAN, including feed-forward neural networks, recurrent neural networks,\u0000and graph neural networks, to quantify their generalization capabilities when\u0000solving Ising models. Moreover, considering the fact that the quantification of\u0000the generalization capabilities of networks on small-scale problems can be used\u0000to predict their relative performance on large-scale problems, our method is of\u0000great significance for assisting in the Neural Architecture Search field of\u0000searching for the optimal network architectures when solving large-scale Ising\u0000models.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the non-Abelian Thouless pumping in a disorder tunable Lieb chain with degenerate flat bands. The results reveal that quasiperiodic disorder will cause a topological phase transition from the trivial (without non-Abelian Thouless pumping) to the non-trivial (with non-Abelian Thouless pumping) phase. The mechanism behind is that the monopole originally outside the topological region can be driven into the topological region due to the introduction of quasiperiodic disorder. Moreover, since the corresponding monopole will turn into a nodal line to spread beyond the boundaries of the topological region, the system with large disorder strength will result in the disappearance of non-Abelian Thouless pumping. Furthermore, we numerically simulate the Thouless pumping of non-Abelian systems, and the evolution results of center of mass' displacement are consistent with the Chern number. Finally, we discuss the localization properties of the system and find that, similar to [PRL 130, 206401(2023)], the inverse Anderson transition does not occur in the system with the increase of quasiperiodic strength, while the system still maintains the coexistence of localized and extended states.
{"title":"Emergent Non-Abelian Thouless Pumping Induced by the Quasiperiodic Disorder","authors":"Sen Huang, Yan-Qing Zhu, Zhi Li","doi":"arxiv-2404.18491","DOIUrl":"https://doi.org/arxiv-2404.18491","url":null,"abstract":"We investigate the non-Abelian Thouless pumping in a disorder tunable Lieb\u0000chain with degenerate flat bands. The results reveal that quasiperiodic\u0000disorder will cause a topological phase transition from the trivial (without\u0000non-Abelian Thouless pumping) to the non-trivial (with non-Abelian Thouless\u0000pumping) phase. The mechanism behind is that the monopole originally outside\u0000the topological region can be driven into the topological region due to the\u0000introduction of quasiperiodic disorder. Moreover, since the corresponding\u0000monopole will turn into a nodal line to spread beyond the boundaries of the\u0000topological region, the system with large disorder strength will result in the\u0000disappearance of non-Abelian Thouless pumping. Furthermore, we numerically\u0000simulate the Thouless pumping of non-Abelian systems, and the evolution results\u0000of center of mass' displacement are consistent with the Chern number. Finally,\u0000we discuss the localization properties of the system and find that, similar to\u0000[PRL 130, 206401(2023)], the inverse Anderson transition does not occur in the\u0000system with the increase of quasiperiodic strength, while the system still\u0000maintains the coexistence of localized and extended states.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vivek Dey, Steffen Kampman, Rafael Gutierrez, Gianaurelio Cuniberti, Pavan Nukala
Brain-like self-assembled networks can infer and analyze information out of unorganized noisy signals with minimal power consumption. These networks are characterized by spatiotemporal avalanches and their crackling behavior, and their physical models are expected to predict and understand their computational capabilities. Here, we use a network theory-based approach to provide a physical model for percolative tunnelling networks, found in Ag-hBN system, consisting of nodes (atomic clusters) of Ag intercalated in the hBN van der Waals layers. By modeling a single edge plasticity through constitutive electrochemical filament formation, and annihilation through Joule heating, we identify independent parameters that determine the network connectivity. We construct a phase diagram and show that a small region of the parameter space contains signals which are long-range temporally correlated, and only a subset of them contains crackling avalanche dynamics. Physical systems spontaneously selforganize to this region for possibly maximizing the efficiency of information transfer.
类脑自组装网络能以最小的功耗从无组织的噪声信号中推断和分析信息。这些网络以时空雪崩和噼啪行为为特征，其物理模型有望预测和理解它们的计算能力。在此，我们采用基于网络理论的方法，为 Ag-hBNsystem 中的渗滤隧道网络提供了一个物理模型，该网络由插在 hBN vander Waals 层中的 Ag 节点（原子团）组成。通过对构成性电化学丝形成和焦耳加热湮灭的单边可塑性建模，我们确定了决定网络连通性的独立参数。我们构建了一个相图，并表明参数空间的一小部分区域包含长程时间相关的信号，其中只有一个子集包含噼啪雪崩动力学。物理系统会自发地在这一区域进行自我组织，从而最大限度地提高信息传递的效率。
{"title":"Network-theory based modeling of avalanche dynamics in percolative tunnelling networks","authors":"Vivek Dey, Steffen Kampman, Rafael Gutierrez, Gianaurelio Cuniberti, Pavan Nukala","doi":"arxiv-2404.18600","DOIUrl":"https://doi.org/arxiv-2404.18600","url":null,"abstract":"Brain-like self-assembled networks can infer and analyze information out of\u0000unorganized noisy signals with minimal power consumption. These networks are\u0000characterized by spatiotemporal avalanches and their crackling behavior, and\u0000their physical models are expected to predict and understand their\u0000computational capabilities. Here, we use a network theory-based approach to\u0000provide a physical model for percolative tunnelling networks, found in Ag-hBN\u0000system, consisting of nodes (atomic clusters) of Ag intercalated in the hBN van\u0000der Waals layers. By modeling a single edge plasticity through constitutive\u0000electrochemical filament formation, and annihilation through Joule heating, we\u0000identify independent parameters that determine the network connectivity. We\u0000construct a phase diagram and show that a small region of the parameter space\u0000contains signals which are long-range temporally correlated, and only a subset\u0000of them contains crackling avalanche dynamics. Physical systems spontaneously\u0000selforganize to this region for possibly maximizing the efficiency of\u0000information transfer.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. V. Afonin, J. C. Qiao, A. S. Makarov, N. P. Kobelev, V. A. Khonik
We performed high-frequency (0.4 to 1.7 MHz) measurements of the internal friction (IF) on 14 bulk metallic glasses (MGs). It is found that 12 of these MGs display relaxation IF peaks at temperatures T= 400-500 K, which are weakly affected by heat treatment within the amorphous state. The corresponding relaxation time is about 0.3 microseconds. This fast relaxation is reported for the first time in the literature. The apparent activation enthalpy for 4 MGs is determined.
{"title":"Fast relaxation in metallic glasses studied by measurements of the internal friction at high frequencies","authors":"G. V. Afonin, J. C. Qiao, A. S. Makarov, N. P. Kobelev, V. A. Khonik","doi":"arxiv-2404.17948","DOIUrl":"https://doi.org/arxiv-2404.17948","url":null,"abstract":"We performed high-frequency (0.4 to 1.7 MHz) measurements of the internal\u0000friction (IF) on 14 bulk metallic glasses (MGs). It is found that 12 of these\u0000MGs display relaxation IF peaks at temperatures T= 400-500 K, which are weakly\u0000affected by heat treatment within the amorphous state. The corresponding\u0000relaxation time is about 0.3 microseconds. This fast relaxation is reported for\u0000the first time in the literature. The apparent activation enthalpy for 4 MGs is\u0000determined.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elizabeth J. Dresselhaus, Alexander Avdoshkin, Zhetao Jia, Matteo Secli, Boubacar Kante, Joel E. Moore
Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a class of $2D$ models generalizing recent experiments on photonic systems. We explore two kinds of localization that emerge in these models: Anderson localization by disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. We find localization properties to depend on the symmetry class within a family of amorphized kagom'{e} tight-binding models, set by a tunable synthetic magnetic field. The flat-band-like degeneracy innate to kagom'{e} lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. For particular values of the field, such states emerge in the amorphous system that were not present on the kagom'{e} lattice in the same field. For generic states, the standard paradigm of Anderson localization is found to apply as expected for systems with particle-hole symmetry (class D), while a similar interpretation does not extend to our results in the general unitary case (class A). The structure of amorphous graphs, which arise in current photonics experiments, allows exact statements about flat-band-like states, including such states that only exist in amorphous systems, and demonstrates how the qualitative behavior of a disordered system can be tuned at fixed graph topology.
{"title":"A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system","authors":"Elizabeth J. Dresselhaus, Alexander Avdoshkin, Zhetao Jia, Matteo Secli, Boubacar Kante, Joel E. Moore","doi":"arxiv-2404.17578","DOIUrl":"https://doi.org/arxiv-2404.17578","url":null,"abstract":"Emerging experimental platforms use amorphousness, a constrained form of\u0000disorder, to tailor meta-material properties. We study localization under this\u0000type of disorder in a class of $2D$ models generalizing recent experiments on\u0000photonic systems. We explore two kinds of localization that emerge in these\u0000models: Anderson localization by disorder, and the existence of compact,\u0000macroscopically degenerate localized states as in many crystalline flat bands.\u0000We find localization properties to depend on the symmetry class within a family\u0000of amorphized kagom'{e} tight-binding models, set by a tunable synthetic\u0000magnetic field. The flat-band-like degeneracy innate to kagom'{e} lattices\u0000survives under amorphousness without on-site disorder. This phenomenon arises\u0000from the cooperation between the structure of the compact localized states and\u0000the geometry of the amorphous graph. For particular values of the field, such\u0000states emerge in the amorphous system that were not present on the kagom'{e}\u0000lattice in the same field. For generic states, the standard paradigm of\u0000Anderson localization is found to apply as expected for systems with\u0000particle-hole symmetry (class D), while a similar interpretation does not\u0000extend to our results in the general unitary case (class A). The structure of\u0000amorphous graphs, which arise in current photonics experiments, allows exact\u0000statements about flat-band-like states, including such states that only exist\u0000in amorphous systems, and demonstrates how the qualitative behavior of a\u0000disordered system can be tuned at fixed graph topology.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chen-Chang Zeng, Zhen Cai, Guang-Heng Wang, Gaoyong Sun
We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{'e}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibilities serve as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the first-excited states, where $mathcal{PT}$ transitions occur, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, the self-normal fidelity susceptibilities near the critical points continue to scale as $N^{2}$. For odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.
{"title":"Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model","authors":"Chen-Chang Zeng, Zhen Cai, Guang-Heng Wang, Gaoyong Sun","doi":"arxiv-2404.16704","DOIUrl":"https://doi.org/arxiv-2404.16704","url":null,"abstract":"We study the critical behaviors of the ground and first excited states in the\u0000one-dimensional nonreciprocal Aubry-Andr{'e}-Harper model using both the\u0000self-normal and biorthogonal fidelity susceptibilities. We demonstrate that\u0000fidelity susceptibilities serve as a probe for the phase transition in the\u0000nonreciprocal AAH model. For ground states, characterized by real eigenenergies\u0000across the entire regime, both fidelity susceptibilities near the critical\u0000points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the\u0000first-excited states, where $mathcal{PT}$ transitions occur, the fidelity\u0000susceptibilities exhibit distinct scaling laws, contingent upon whether the\u0000lattice consists of even or odd sites. For even lattices, the self-normal\u0000fidelity susceptibilities near the critical points continue to scale as\u0000$N^{2}$. For odd lattices, the biorthogonal fidelity susceptibilities diverge,\u0000while the self-normal fidelity susceptibilities exhibit linear behavior,\u0000indicating a novel scaling law.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a quantum perceptron implemented on a quantum circuit using a repeat until method. We evaluate this from the perspective of capacity, one of the performance evaluation measures for perceptions. We assess a Gardner volume, defined as a volume of coefficients of the perceptron that can correctly classify given training examples using the replica method. The model is defined on the quantum circuit. Nevertheless, it is straightforward to assess the capacity using the replica method, which is a standard method in classical statistical mechanics. The reason why we can solve our model by the replica method is the repeat until method, in which we focus on the output of the measurements of the quantum circuit. We find that the capacity of a quantum perceptron is larger than that of a classical perceptron since the quantum one is simple but effectively falls into a highly nonlinear form of the activation function.
{"title":"Storage Capacity Evaluation of the Quantum Perceptron using the Replica Method","authors":"Mitsuru Urushibata, Masayuki Ohzeki","doi":"arxiv-2404.14785","DOIUrl":"https://doi.org/arxiv-2404.14785","url":null,"abstract":"We investigate a quantum perceptron implemented on a quantum circuit using a\u0000repeat until method. We evaluate this from the perspective of capacity, one of\u0000the performance evaluation measures for perceptions. We assess a Gardner\u0000volume, defined as a volume of coefficients of the perceptron that can\u0000correctly classify given training examples using the replica method. The model\u0000is defined on the quantum circuit. Nevertheless, it is straightforward to\u0000assess the capacity using the replica method, which is a standard method in\u0000classical statistical mechanics. The reason why we can solve our model by the\u0000replica method is the repeat until method, in which we focus on the output of\u0000the measurements of the quantum circuit. We find that the capacity of a quantum\u0000perceptron is larger than that of a classical perceptron since the quantum one\u0000is simple but effectively falls into a highly nonlinear form of the activation\u0000function.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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