Ignacio Garcia-Mata, Dima L. Shepelyansky
We study effects of weak nonlineary on localization of waves in disordered Stark ladder corresponding to propagation in presence of disorder and a static field. Our numerical results show that nonlinearity leads to delocalization with subdiffusive spreading along the ladder. The exponent of spreading remains close to its value in absence of the static field.
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The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how…
Quantum Simulation of Detuning-Controlled Proximity-Induced Localization and Reentrant Delocalization in a Quasiperiodic Ladder
本研究通过量子模拟证明，在准周期梯子中仅对一条腿施加失谐即可诱导邻近腿局域化，并随失谐增大实现退局域化再入，提供可编程控制局域化的新机制。
The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize differ…
Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders
该研究针对一维有限高度Wannier-Stark梯，精确确定了遍历态与弱遍历态的临界能量，揭示了相图特征及临界能量对梯高的依赖，发现可通过非零势间隔调控遍历态数量，为无无序系统研究提供参考。
We study numerically the linear optical response of a quasiparticle moving on a one-dimensional disordered lattice in the presence of a linear bias. The random site potential is assumed to be long-range-correlated with a power-law spectral density $S(k) \sim 1/k^α$, $α> 0$. This type of correlations results in a phase of extended states at the band center, provided $α$ is larger than a critical value $α_c$ [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. \textbf{81}, 3735 (1998)]. The width of the delocalized phase can be tested by applying an external electric field: Bloch-like oscillat…
We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the superspin ladder and the corresponding supersymmetric nonlinear sigma model allows to establish the phase diagram of the network model, and the form of the critical line of the weak-field IQH transition. Our results confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. We apply the suspe…
Lateral Shift as a Control Knob for Localization Transitions in a Quasiperiodic Ladder
本文研究准周期梯子中两腿间横向位移对局域化-去局域化转变的调控作用，发现横向位移等效产生倒易空间磁通，可实现磁通增强/抑制局域化及重入转变，并通过能带分析揭示相边界。
Wannier-Stark localization in one-dimensional amplitude-chirped lattices
本文研究一维振幅啁啾晶格中的Wannier-Stark局域化，发现q=4时出现能量依赖的扩展态，奇数q非厄米系统中部分WS阶梯二重简并，揭示了厄米与非厄米晶格中的新局域化现象。
Using numerically exact methods we study transport in an interacting spin chain which for sufficiently strong spatially constant electric field is expected to experience Stark many-body localization. We show that starting from a generic initial state, a spin-excitation remains localized only up to a finite delocalization time, which depends exponentially on the size of the system and the strength of the electric field. This suggests that bona fide Stark many-body localization occurs only in the thermodynamic limit. We also demonstrate that the transient localization in a finite system and for …
Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
本文利用转移矩阵方法研究了一维非互易 Wannier-Stark 晶格中赝迁移率边与多重态的命运，揭示了非互易性对各态历经与非各态历经态边界、拓扑点隙形成及混合态局域化的影响，并通过波包动力学进行检测，拓宽了对非厄米系统无序局域化的理解。
Stark localization near Aubry-André criticality
本文研究AA模型临界点附近的Stark局域化，通过局域化长度、IPR和能隙标度揭示其区别于纯AA与纯Stark模型的临界行为，并提出利用准周期势增强量子临界传感器对弱Stark场的估计精度。
Absence of localization in interacting spin chains with a discrete symmetry
本文证明具有镜像与自旋翻转组合对称性的自旋链在零磁化和无限温度下存在有限自旋输运，并通过Stark多体局域化等数值实验表明离域化在所有能量密度下成立且对对称性破缺鲁棒。
The existence of localization and mobility edges in one-dimensional lattices is commonly thought to depend on disorder (or quasidisorder). We investigate localization properties of a disorder-free lattice subject to an equally spaced electric field. We analytically show that, even though the model has no quenched disorder, this system manifests an exact mobility edge and the localization regime extends to weak fields, in contrast to gigantic field for the localization of a usual Stark lattice. For strong fields, the Wannier-Stark ladder is recovered and the number of localized eigenstates is i…
Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$…
We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pmμ$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $μ$, while with an additional static field $ε$ we find oscillatory motion with a superposition of frequencies $(ε\pm μ)$. On the other hand, when the jump rate is `rapid', and in the absence of a stati…
From ergodicity to Stark many-body localization in spin chains with single-ion anisotropy
本研究探讨了具有单离子各向异性的自旋链中的Stark多体局域化现象，发现近恒定梯度磁场和单离子各向异性均可抑制热化，且两者竞争时有利于离域化，为局域化机制提供了新见解。
The fate of Wannier-Stark localization and skin effect in periodically driven non-Hermitian quasiperiodic lattices
本文研究周期驱动非厄米准周期晶格，发现慢调制电场产生多迁移率边新相，快驱动恢复无WS局域化，且驱动下趋肤效应出现并呈多分形。
Stark many-body localization (SMBL) is a phenomenon observed in interacting systems with a nearly uniform spatial gradient applied field. Contrasting to the traditional many-body localization phenomenon, SMBL does not require disorder. Here we investigate SMBL in a spin-$1/2$ described by a Heisenberg model including a next-nearest-neighbor exchange coupling. By employing an exact diagonalization approach and time evolution calculation we analyze both level spacing ratio (LSR) statistics of the Hamiltonian model as well as the dynamics of the system from a given initial state. Our results reve…
Quantum criticality and Kibble-Zurek scaling in the Aubry-André-Stark model
本文研究了Aubry-André-Stark模型中的量子临界性与Kibble-Zurek标度，发现离域-定域化转变的新临界指数，并验证了驱动动力学遵循包含双标度变量的KZS形式。
Investigating Stark many-body localization with continuous unitary transformation flows
采用Tensorflow Equations方法研究均匀电场下相互作用费米子系统的遍历性到局域化转变，发现1D中存在随系统尺寸消失的有限场局域化转变，而2D中特征不明显且有限尺寸效应强。
Thermalization in many-body systems can be inhibited by the application of a linearly increasing potential, which is known as Stark many-body localization. Here we investigate the fate of this phenomenon on a two-dimensional disorder-free lattice with up to $24 \times 6$ sites. Similar to the one-dimensional case, "density-polarized" regions can act as bottlenecks for transport and thermalization on laboratory timescales. However, compared to the one-dimensional case, a substantially stronger potential gradient is needed to prevent thermalization when an extra spatial dimension is involved. Th…
Localization and mobility edges in non-Hermitian disorder-free lattices
本文研究非厄米马赛克 Stark 晶格中电场、Stark 局域化、迁移率边与非厄米趋肤效应的耦合，解析并数值揭示不同马赛克周期下的临界场、拓扑转变及动力学特征。
Thermally induced localization of dopants in a magnetic spin ladder
本研究发现磁性自旋梯子中掺杂空穴可因热自旋涨落诱导的有效无序势发生新型安德森局域化，分析了不同耦合、温度下的局域化行为，并提出里德堡缀饰原子实验可验证该现象。
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