A. Yu. Khrennikov, S. V. Kozyrev
Free evolution for quantum particle in general ultrametric space is considered. We find that if mean zero wave packet is localized in some ball in the ultrametric space then its evolution remains localized in the same ball.
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We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric space for the walk. This result presents a striking contrast to the classical random walk case. Moreover we clarify a difference between the ultrametric space and other graphs, such as cycle graph, line, hypercube and complete graph, for the localization of the quantum case. Our quantum walk may be useful for a quantum search algorithm on a tree-like hierar…
Similarity between a many-body quantum avalanche model and the ultrametric random matrix model
本文将量子雪崩玩具模型与随机矩阵理论中的超度量系综联系起来，猜想并数值验证了两者在临界点位置、Fock空间局域化、临界流形上的多重分形本征矢及可调谱统计等方面具有共同特征。
We identify a new parameter that controls the localization length in a driven quantum system. This parameter results from an additional quantum degree of freedom. The center-of-mass motion of a two-level ion stored in a Paul trap and interacting with a standing wave laser field exhibits this phenomenon. We also discuss the influence of spontaneous emission.
Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
本研究利用无副本的实时Dyson-Keldysh形式体系，揭示了长程量子自旋玻璃的晚期动力学与Parisi超度量结构、副本对称性破缺的关联，并通过球形量子p-spin模型验证了方法的适用性。
Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.
Slow growth of quantum magic in disorder-free Stark many-body localization
研究通过稳定器瑞尼熵量化无杂质量子多体局域化中的量子魔性，发现其在强倾斜区域缓慢增长并最终饱和，揭示了从厄尔戈迪克动力学向受限局域化的过渡。
The properties of the s-wave for a quasi-free particle with position-dependent mass(PDM) have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in $D$ dimensions except D=1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction which may be attractive in some cases. The analytical expressions of the eigenf…
Impurity-induced loss bursts from anomalous scale-free localization in a non-Hermitian dissipative lattice
研究通过非厄密特耗散交叉缝 lattice 识别异常无尺度局域化及杂质诱导的损耗脉冲，利用局部基底旋转将模型映射到有效的非厄密特 Su-Schrieffer-Heeger lattice，其中局部杂质作为可调的有效边界，通过调整杂质强度η连接两个有效开放边界条件极限，通过广义边界条件区域和杂质自由周期边界条件点，展示了无尺度局域化与可控耗散动力学的联系。
Entanglement phases and phase transitions in monitored free fermion system due to localizations
研究受监控自由费米系统中局部化对纠缠相及相变的影响，揭示测量与局部化共同作用下的纠缠相界特性。
Critical Non-Hermitian Skin Effect and Scale-Free Localization Morphing in Bilocally Coupled Hatano-Nelson Chains
研究双链局域耦合的Hatano-Nelson链，发现强耦合下仍存在临界非厄米趋肤效应，通过局域杂化碎片化希尔伯特空间产生无标度趋肤态，开辟了非厄米临界行为的新途径。
From scale-free to Anderson localization: a size-dependent transition
研究非厄米系统中标度无关局域态在无序作用下转变为安德森局域态，发现该转变依赖于系统尺寸，与Hatano-Nelson模型不同。
Edge burst effect and scale-free localization
本文研究有损晶格中的非厄米边缘突发效应，通过弱耦合两个具有双极NHSE的晶格实现双极无标度局域化，并证实无趋肤效应时仍可发生边缘突发。
This work develops a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with PBCs, OBCs and even their interpolations being special cases across a whole range of boundary impurity strengths. As the impurity strength is tuned, the localization of steady states can assume very rich behavior, including the expected non-Hermitian skin effect, Bloch-like states albeit broken translational invariance, and surprisingly, scale-free accumulation along or even against the direction of non-reciprocity. We further uncover the possibility of the co-existence of non-Hermitian ski…
Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
研究在非厄密链中同时实现皮肤效应和临界性，揭示了莫比乌斯边界条件下本征态的两种不同局域化行为及其相互转换机制。
We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which the classical ultrametric random walk as well as the quantum walk can be treated in parallel by using a "coined" walk with internal degrees of freedom. For the random walk, this amounts to a $2^{\rm nd}$-order Markov process with a \emph{stochastic} coin, better known as an (anti-)persistent walk. When this coin varies spatially in the hierarchical manner of "…
Emerging dynamical constraints resulting from inter-site interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the $1/r^3$ tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body …
Disorder-free localization is a paradigm of nonergodicity in translation-invariant quantum many-body systems hosting gauge symmetries. The quench dynamics starting from simple initial states, which correspond to extensive superpositions of gauge superselection sectors, exhibits many-body localization with the system dynamically inducing its own disorder. An open question concerns the stability of disorder-free localization in the presence of gauge-breaking errors, and whether processes due to the latter can be controllably suppressed. Here, we show that translation-invariant \textit{single-bod…
The phenomenon of Many-Body Stark Localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well known many body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches poissonian value as characteristic for localized situations but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may…
We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice. We illustrate that the coupling has a dramatic effect on localization properties, even with a s…
We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the tunneling effect. The decoherence happens even for cases that the influence is from a particle of very small mass, and it has virtually no effect in the corresponding classical dynamics. There are cases similar to dynamical localization that the suppressed tunneling rate is several times smaller than the classical counterpart. This result is relevant for understand…
Scale-free localization and PT symmetry breaking from local non-Hermiticity
本文证明厄米晶格中的局部非厄米扰动会普遍诱导无标度局域化，并揭示了其与PT对称性破缺的关联及精确破缺能量窗口的能带条件。
Disorder-free localization is a paradigm of strong ergodicity breaking that has been shown to occur in global quenches of lattice gauge theories when the system is initialized in a superposition over an extensive number of gauge sectors. Here, we show that preparing the system in a thermal Gibbs ensemble without any coherences between different gauge sectors also gives rise to disorder-free localization, with temperature acting as a disorder strength. We demonstrate our findings by calculating the quench dynamics of the imbalance of thermal ensembles in both $\mathrm{U}(1)$ and $\mathbb{Z}_2$ …
Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach
本文在量子伯努利噪声框架下研究超立方体上自旋耦合量子行走，提出无无序局域化的谱判据，并在特定Grover行走中构造非均匀不动点，证明该现象发生。
Disorder-free localization in translation-invariant gauge theories presents a counterintuitive yet powerful framework of ergodicity breaking in quantum many-body physics. The fragility of this phenomenon in the presence of gauge-breaking errors has recently been addressed, but no scheme has been able to reliably stabilize disorder-free localization through all accessible evolution times while preserving the disorder-free property. Here, we introduce the concept of \textit{Stark gauge protection}, which entails a linear sum in gauge-symmetry local (pseudo)generators weighted by a Stark potentia…
A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of gra…
Dissipation-Enhanced Localization in a Disorder-Free $\mathbb{Z}_2$ Lattice Gauge System
本文研究耦合马尔可夫环境的$\mathbb{Z}_2$格点规范模型，发现量子耗散能增强无序自由局域化，使初始状态记忆比幺正演化更稳健，且适用于多种初始态，表明耗散可稳定非遍历行为。
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved mom…
Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. Specifically, we prove nonergodic behavior in the quantum link model by obtaining a rigorous bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side o…
Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors. Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation-invariant. In a recent work [Halimeh, Zhao, Hauke, and Knolle, arXiv:2111.02427], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in $\mathrm{U}(1)$ gauge theories against gauge erro…
Boundary-sensitive non-Hermiticity of Floquet Hamiltonian: spectral transition and scale-free localization
本文提出一种边界敏感的PT对称破缺机制，通过设计时间周期性驱动协议，揭示Floquet哈密顿量在周期边界条件下的厄米性与开放边界条件下的非厄米性差异，并展示PT破缺相中出现的无标度局域化现象。
Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in $1+1$D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in $2+1$D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in $2+1$D LGT…
Role of flavor degrees of freedom in quantum simulations of disorder-free localization
该研究通过Google量子AI实验结合数值模拟，揭示味自由度的局域无序谱而非仅无序强度，决定无无序定域化，二元与多能级无序的定域化行为存在本质差异。
Disorder-Free Localization for Benchmarking Quantum Computers
本文提出将无序局域化（DFL）的典型模型通过高效的三比特门编码实现于基于门的量子计算机上，利用关联传播缺失与可调纠缠增长至体积律作为基准测试平台，为可扩展量子计算机的能力提供严格预测与理想测试。
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