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Multifractality and Fock-space localization in many-body localized states: One-particle density matrix perspective 多体定域态中的多重分形和fock空间定域:单粒子密度矩阵视角
Pub Date : 2021-04-19 DOI: 10.1103/PhysRevB.103.214206
Takahiro Orito, K. Imura
Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_q$ is employed; it has been claimed that $D_q$ shows a jump from the delocalized value $D_q=1$ in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value $0
多体定位(MBL)在Fock空间中具有很好的特征。为了量化这种Fock空间局部化的程度,采用多重分形维数$D_q$;有人声称$D_q$在ETH相(ETH:本征态热化假设)中显示出从离域值$D_q=1$到ETH-MBL跃迁的较小值$0
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引用次数: 5
Thouless Energy Across Many-Body Localization Transition in Floquet Systems. Floquet系统多体局部化转换中的无能量。
Pub Date : 2020-12-31 DOI: 10.1103/PhysRevB.104.L081112
M. Sonner, Maksym Serbyn, Z. Papi'c, D. Abanin
The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g. typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, the Thouless energy tends to a value independent of system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of the Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting, and yields new insights into the MBL transition in Floquet systems.
索利斯能量的概念在安德森局域化理论中起着核心作用。研究了Floquet模型中多体局部化(MBL)跃迁过程中Thouless能量的标度。我们结合了在跃迁的遍历侧可靠的方法(例如,频谱形式因子)和在MBL侧工作的方法(例如,局部算子的典型矩阵元素)来获得整个跃迁的Thouless能量行为的完整图像。在遍历侧,索利斯能量趋向于一个与系统大小无关的值,而在过渡时,它变得与能级间距相当。不同的探针在其重叠的适用范围内产生一致的索利斯能量估计,使过渡点的位置几乎不受有限大小漂移的影响。这项工作建立了多体环境中索利斯能量的不同定义之间的联系,并对Floquet系统中的MBL跃迁产生了新的见解。
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引用次数: 8
Duality between two generalized Aubry-André models with exact mobility edges 具有精确迁移边的两个广义aubry - andr<s:1>模型之间的对偶性
Pub Date : 2020-12-17 DOI: 10.1103/PhysRevB.103.174205
Yucheng Wang, Xu Xia, Yongjian Wang, Zuohuan Zheng, Xiong-Jun Liu
A mobility edge (ME) in energy separating extended from localized states is a central concept in understanding various fundamental phenomena like the metal-insulator transition in disordered systems. In one-dimensional quasiperiodic systems, there exist a few models with exact MEs, and these models are beneficial to provide exact understanding of ME physics. Here we investigate two widely studied models including exact MEs, one with an exponential hopping and one with a special form of incommensurate on-site potential. We analytically prove that the two models are mutually dual, and further give the numerical verification by calculating the inverse participation ratio and Husimi function. The exact MEs of the two models are also obtained by calculating the Lyapunov exponents and using the duality relations. Our result may provide insight into realizing and observing exact MEs in both theory and experiment.
从局域态扩展的能量分离中的迁移边缘(ME)是理解无序系统中金属-绝缘体跃迁等各种基本现象的中心概念。在一维准周期系统中,存在一些具有精确MEs的模型,这些模型有助于精确理解MEs物理。在这里,我们研究了两种广泛研究的模型,包括精确MEs,一个具有指数跳变和一个具有特殊形式的不相称现场势。分析证明了两种模型是相互对偶的,并通过计算逆参与率和胡思米函数给出了数值验证。通过计算李雅普诺夫指数和利用对偶关系,得到了两种模型的精确MEs。我们的研究结果可以为在理论和实验中实现和观察精确的MEs提供见解。
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引用次数: 13
Curvature-driven ac-assisted creep dynamics of magnetic domain walls 曲率驱动的交流辅助磁畴壁蠕变动力学
Pub Date : 2020-12-17 DOI: 10.1103/PhysRevB.103.L220409
P. Domenichini, F. Parı́s, M. Capeluto, M. Granada, J. George, G. Pasquini, A. Kolton
The dynamics of micrometer-sized magnetic domains in ultra-thin ferromagnetic films is so dramatically slowed down by quenched disorder that the spontaneous elastic tension collapse becomes unobservable at ambient temperature. By magneto-optical imaging we show that a weak zero-bias AC magnetic field can assist such curvature-driven collapse, making the area of a bubble to reduce at a measurable rate, in spite of the negligible effect that the same curvature has on the average creep motion driven by a comparable DC field. An analytical model explains this phenomenon quantitatively.
超薄铁磁薄膜中微米级磁畴的动力学被淬火无序极大地减缓,以至于在室温下无法观察到自发弹性张力崩溃。通过磁光成像,我们发现微弱的零偏置交流磁场可以帮助这种曲率驱动的坍塌,使气泡的面积以可测量的速率减少,尽管相同的曲率对由类似的直流场驱动的平均蠕变运动的影响可以忽略不计。一个分析模型定量地解释了这一现象。
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引用次数: 0
Relationship between two-level systems and quasi-localized normal modes in glasses 双能级系统与玻璃准定域法模的关系
Pub Date : 2020-12-14 DOI: 10.1103/PhysRevMaterials.5.055602
D. Khomenko, D. Reichman, F. Zamponi
Tunnelling Two-Level Systems (TLS) dominate the physics of glasses at low temperatures. Yet TLS are extremely rare and it is extremely difficult to directly observe them $it{in , silico}$. It is thus crucial to develop simple structural predictors that can provide markers for determining if a TLS is present in a given glass region. It has been speculated that Quasi-Localized vibrational Modes (QLM) are closely related to TLS, and that one can extract information about TLS from QLM. In this work we address this possibility. In particular, we investigate the degree to which a linear or non-linear vibrational mode analysis can predict the location of TLS independently found by energy landscape exploration. We find that even though there is a notable spatial correlation between QLM and TLS, in general TLS are strongly non-linear and their global properties cannot be predicted by a simple normal mode analysis.
隧道双能级系统(TLS)在低温下的玻璃物理学中占主导地位。然而,TLS非常罕见,并且很难直接观察到它们。因此,开发简单的结构预测器是至关重要的,它可以提供标记,以确定在给定的玻璃区域中是否存在TLS。人们推测准局域振动模式(quasi - localization vibrational Modes, QLM)与TLS密切相关,并且可以从QLM中提取有关TLS的信息。在这项工作中,我们解决了这种可能性。特别是,我们研究了线性或非线性振动模式分析在多大程度上可以预测由能量景观勘探独立发现的TLS的位置。我们发现,尽管QLM和TLS之间存在显著的空间相关性,但总体上TLS是强非线性的,它们的整体性质不能通过简单的正态分析来预测。
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引用次数: 8
Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems 无序SU(2)-对称Floquet系统的扩展非遍历区和自旋亚扩散
Pub Date : 2020-12-01 DOI: 10.1103/physrevb.102.214205
Zhi-Cheng Yang, Stuart Nicholls, M. Cheng
We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite temperature spin autocorrelation function decays at long times as $t^{-beta}$ with $beta < 0.5$, indicating subdiffusive transport at strong disorders.
我们研究了一维无序SU(2)对称Floquet模型中的热化和量子动力学,其中多体局域相被非阿贝尔对称所禁止。尽管缺乏局域化,我们发现在强无序状态下系统表现出非热行为的扩展非过能状态。在强无序状态下,能级间隔统计量既不表现Wigner-Dyson分布,也不表现泊松分布,谱形式因子也不表现随机矩阵理论的早期线性增长特征。Floquet本征态的平均纠缠熵是亚热的,尽管违反了与系统尺寸成比例的面积定律。我们进一步计算了局部观测值的期望值,并发现了与本征态热化假设的强烈偏差。无限温度自旋自相关函数在长时间衰减为$t^{-beta}$且$beta < 0.5$,表明在强失序下存在亚扩散输运。
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引用次数: 4
Transmission of waves through a pinned elastic medium 波通过固定弹性介质的传输
Pub Date : 2020-12-01 DOI: 10.1103/PhysRevB.103.224211
Tsuyoshi Yamamoto, L. Glazman, M. Houzet
We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian correlations, acting on propagating waves. We find signatures of the correlations in the wave transmission in a wide frequency range, which covers both the weak and strong localization regimes. Our theory works for any elastic medium. One-dimensional Josephson junction arrays provide an example where our results can be applied to detect and study the insulating "Bose-glass" phase using the microwave impedance data.
我们研究了弹性波在一维随机相位正弦戈登模型描述的无序区域的散射。集体钉住产生一个有效的静态无序势,具有普适和非高斯相关,作用于传播波。在较宽的频率范围内,我们发现了波传播中相关的特征,包括弱局域化和强局域化。我们的理论适用于任何弹性介质。一维约瑟夫森结阵列提供了一个例子,我们的结果可以应用于利用微波阻抗数据检测和研究绝缘“玻色-玻璃”相位。
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引用次数: 1
Disorder in dissipation-induced topological states: Evidence for a different type of localization transition 耗散引起的拓扑状态的紊乱:一种不同类型的局域转换的证据
Pub Date : 2020-11-19 DOI: 10.1103/PhysRevB.103.L241401
Alon Beck, M. Goldstein
The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. In this work we shed new light on this issue by studying the effect of disorder on recently-introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite size scaling methods we show that the critical exponent $nu$ describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the non-dissipative part of the dynamics. This indicates a new nonequilibrium quantum critical universality class accessible in cold-atom experiments.
对非平衡态量子相变的探索常常受到驱动和耗散产生有效温度的趋势的阻碍,从而导致经典行为。在这项工作中,我们通过研究无序对最近引入的耗散诱导的陈氏拓扑态的影响,以及检查厄米稳态密度矩阵或纠缠哈密顿量的特征模,为这个问题提供了新的思路。我们发现,与平衡相似,每个朗道带在其中心附近有一个离域能级。然而,使用三种不同的有限尺寸标度方法,我们表明,如果在动力学的非耗散部分引入无序,描述局域化长度在接近离域状态时的散度的临界指数$nu$与平衡值显着不同。这为冷原子实验提供了一种新的非平衡态量子临界普适性。
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引用次数: 5
Suppression of transport anisotropy at the Anderson localization transition in three-dimensional anisotropic media 三维各向异性介质中安德森局域化转变中输运各向异性的抑制
Pub Date : 2020-11-18 DOI: 10.1103/physrevb.102.220201
Antton Goïcoechea, S. Skipetrov, J. Page
We study the transport of classical waves through three-dimensional (3D) anisotropic media close to the Anderson localization transition. Time-, frequency-, and position-resolved ultrasonic measurements are performed on anisotropic slab-shaped mesoglass samples to probe the dynamics and the anisotropy of the multiple scattering halo, and hence to investigate the influence of disorder on the nature of wave transport and its anisotropy. These experiments allow us to address conflicting theoretical predictions that have been made about whether or not the transport anisotropy is affected by the interference effects that lead to Anderson localization. We find that the transport anisotropy is significantly reduced as the mobility edge is approached---a behavior similar to the one predicted recently for matter waves in infinite anisotropic 3D media.
我们研究了经典波在接近安德森局域化跃迁的三维各向异性介质中的输运。对各向异性板状介玻璃样品进行了时间、频率和位置分辨超声测量,以探测多重散射晕的动力学和各向异性,从而研究无序对波输运性质及其各向异性的影响。这些实验使我们能够解决关于输运各向异性是否受到导致安德森局域化的干扰效应影响的相互矛盾的理论预测。我们发现,随着迁移率边缘的接近,输运各向异性显著降低——这种行为类似于最近对无限各向异性三维介质中物质波的预测。
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引用次数: 4
Radio-Frequency Multiply-and-Accumulate Operations with Spintronic Synapses 自旋电子突触的射频乘法和累加运算
Pub Date : 2020-11-16 DOI: 10.1103/PHYSREVAPPLIED.15.034067
N. Leroux, Danijela Marković, Erwann Martin, Teodora Petrisor, D. Querlioz, A. Mizrahi, J. Grollier
Exploiting the physics of nanoelectronic devices is a major lead for implementing compact, fast, and energy efficient artificial intelligence. In this work, we propose an original road in this direction, where assemblies of spintronic resonators used as artificial synapses can classify an-alogue radio-frequency signals directly without digitalization. The resonators convert the ra-dio-frequency input signals into direct voltages through the spin-diode effect. In the process, they multiply the input signals by a synaptic weight, which depends on their resonance fre-quency. We demonstrate through physical simulations with parameters extracted from exper-imental devices that frequency-multiplexed assemblies of resonators implement the corner-stone operation of artificial neural networks, the Multiply-And-Accumulate (MAC), directly on microwave inputs. The results show that even with a non-ideal realistic model, the outputs obtained with our architecture remain comparable to that of a traditional MAC operation. Us-ing a conventional machine learning framework augmented with equations describing the physics of spintronic resonators, we train a single layer neural network to classify radio-fre-quency signals encoding 8x8 pixel handwritten digits pictures. The spintronic neural network recognizes the digits with an accuracy of 99.96 %, equivalent to purely software neural net-works. This MAC implementation offers a promising solution for fast, low-power radio-fre-quency classification applications, and a new building block for spintronic deep neural net-works.
利用纳米电子器件的物理特性是实现紧凑、快速和节能的人工智能的主要途径。在这项工作中,我们在这个方向上提出了一条原创的道路,其中自旋电子谐振器组件用作人工突触,可以直接对模拟射频信号进行分类,而无需数字化。谐振器通过自旋二极管效应将射频输入信号转换成直流电压。在这个过程中,他们将输入信号乘以突触权重,这取决于它们的共振频率。我们通过从实验设备中提取参数的物理模拟证明,频率复用的谐振器组件直接在微波输入上实现了人工神经网络的基石操作,即乘法和累加(MAC)。结果表明,即使在非理想的现实模型下,我们的架构所获得的输出仍然与传统的MAC操作相当。我们使用传统的机器学习框架和描述自旋电子谐振器物理特性的方程,训练单层神经网络对编码8x8像素手写数字图像的射频信号进行分类。自旋电子神经网络对数字的识别准确率达到99.96%,相当于单纯的软件神经网络。该MAC实现为快速、低功耗射频分类应用提供了一个有前途的解决方案,并为自旋电子深度神经网络提供了一个新的构建块。
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引用次数: 13
期刊
arXiv: Disordered Systems and Neural Networks
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