The Behavior of Many-body Localization in the Periodically Driven Heisenberg XXX Model

International Journal of Theoretical Physics - In this paper, we use exact matrix diagonalization to research property of the many-body localization (MBL) in the disordered Heisenberg XXX model...     

Non-ergodic states induced by impurity levels in quantum spin chains

The semi-infinite XY spin chain with an impurity at the boundary has been chosen as a prototype of interacting many-body systems to test for non-ergodic behavior. The model is exactly solvable in analytic way in the thermodynamic limit, where energy eigenstates and the spectrum are obtained in closed form. In addition of a continuous band, localized states may split off from the continuum, for some values of the impurity parameters. In the next step, after the preparation of an arbitrary non-equilibrium state, we observe the time evolution of the site magnetization. Relaxation properties are described by the long-time behavior, which is estimated using the stationary phase method. Absence of localized states defines an ergodic region in parameter space, where the system relaxes to a homogeneous magnetization. Out of this region, impurity levels split from the band, and localization phenomena may lead to non-ergodicity.     

Finite-size scaling exponents of the Lipkin-Meshkov-Glick model

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.     

Machine Learning for Many-Body Localization Transition

We employ the methods of machine learning to study the many-body localization(MBL) transition in a 1D random spin system. By using the raw energy spectrum without pre-processing as training data, it is shown that the MBL transition point is correctly predicted by the machine. The structure of the neural network reveals the nature of this dynamical phase transition that involves all energy levels, while the bandwidth of the spectrum and nearest level spacing are the two dominant patterns and the latter stands out to classify phases. We further use a comparative unsupervised learning method, i.e., principal component analysis, to confirm these results.     

Non-Hermitian topological Anderson insulators

Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.     

Theory of many-body localization in periodically driven systems

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.     

Experimental Observation of the Ground-State Geometric Phase of Three-Spin XY Model

The geometric phase has become a fundamental concept in many fields of physics since it was revealed.Recently,the study of the geometric phase has attracted considerable attention in the context of quantum phase transition,where the ground state properties of the system experience a dramatic change induced by a variation of an external parameter.In this work,we experimentally measure the ground-state geometric phase of the threespin XY model by utilizing the nuclear magnetic resonance technique.The experimental results indicate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body systems.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Periodically driven ergodic and many-body localized quantum systems

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.     

The reservoir learning power across quantum many-body localization transition

Harnessing the quantum computation power of the present noisy-intermediate-size-quantum devices has received tremendous interest in the last few years. Here we study the learning power of a one-dimensional long-range randomly-coupled quantum spin chain, within the framework of reservoir computing. In time sequence learning tasks, we find the system in the quantum many-body localized (MBL) phase holds long-term memory, which can be attributed to the emergent local integrals of motion. On the other hand, MBL phase does not provide sufficient nonlinearity in learning highly-nonlinear time sequences, which we show in a parity check task. This is reversed in the quantum ergodic phase, which provides sufficient nonlinearity but compromises memory capacity. In a complex learning task of Mackey–Glass prediction that requires both sufficient memory capacity and nonlinearity, we find optimal learning performance near the MBL-to-ergodic transition. This leads to a guiding principle of quantum reservoir engineering at the edge of quantum ergodicity reaching optimal learning power for generic complex reservoir learning tasks. Our theoretical finding can be tested with near-term NISQ quantum devices.     

双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应

研究了双势阱玻色-爱因斯坦凝聚体系(BEC)的自俘获现象(self-trapping). 在平均场近似下通过相平面(phase space)分析的方法研究了两种自俘获的机理：1)势阱中的粒子数在平衡位置附近振动，而相对相位随时间单调变化(running-phase); 2) 势阱中的粒子数和相对相位都在平衡点附近振动. 研究了周期调制场对自俘获现象的影响，发现发生自俘获现象的相变参数能够被周期场非常有效的调制，从而在弱相互作用BEC体系中也可以观察到自俘获现象. 还研究了多体量子涨落对自俘获现象的影响，讨论了在现有的实验条件下对凝聚体自俘获现象进行观察和周期调制. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 周期调制     

Magnetic properties and magnetic interactions in chromium-rich Cr-Fe alloys

The results of magnetization measurements on several disordered b.c.c. Cr-Fe alloys with 1, 1.5, 2.4, 5.3, 12 and 14.2 at % of Fe are reported. The measurements were done in pulsed magnetic fields up to 330 kOe and for the two last alloys also in static magnetic fields up to 44 kOe as in function of temperature. The data support the recently proposed model of magnetic interactions in these alloys by Friedel and Hedman. For the alloys with iron concentration equal to and greater than 2.4 at % we observe, at low temperature, the occurence of a ferromagnetic component in the magnetization curves saturating at an external field of about 140 kOe arising from ferromagnetic iron-rich cluster. At liquid helium temperature the localized iron moments within such iron clusters increase from 1.4μ_B to 1.8μ_b when the iron concentration changes from 2.4 at % to 14.2 at %. At higher iron concentrations we observe a spin glass like transition connected with a freezing of ferromagnetic clusters at very low temperature. Both phase boundaries connected with supermagnetic-paramagnetic and superamagnetis-spin glass like transitions are given.     

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an instanton liquid model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.     

Unveiling Operator Growth Using Spin Correlation Functions

In this paper, we study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK)-based quench protocol, we show that the time evolution of simple spin-spin correlation functions is highly sensitive to the degree of k-locality of the corresponding operators, once an appropriate set of fundamental fields is identified. By tracking the time-evolution of specific spin-spin correlation functions and their decay, we argue that it is possible to distinguish between operator-hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems. Such an observation, in turn, could constitute a promising tool to probe the emergence of chaotic behavior, rather accessible in state-of-the-art quench setups.     

Supercooling of the disordered vortex lattice in Bi(2)Sr(2)CaCu(2)O(8+delta)

Time-resolved local induction measurements near the vortex lattice order-disorder transition in optimally doped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals show that the high-field, disordered phase can be quenched to fields as low as half the transition field. Over an important range of fields, the electrodynamical behavior of the vortex system is governed by the coexistence of ordered and disordered vortex phases in the sample. We interpret the results as supercooling of the high-field phase and the possible first-order nature of the order-disorder transition at the "second magnetization peak."     

Anderson localization and non-linear sigma model with graded symmetry

A model of disordered single-particle systems is studied with regard to properties of the localized phase. Defined over a graded coset space, this model represents the correct non-perturbative extension of a non-linear sigma model introduced into localization theory by Schäfer and Wegner. An integral theorem is proven which allows us to change variables and execute the Grassmann integrations rather easily. In the localized phase, the invariant two-point functions are singular on the real axis. It is shown how to extract the singular contribution before evaluation of the functional integral. This is used to derive Efetov's solution of the Cayley tree model in a simple and transparent manner. Finally, a Monte Carlo algorithm is outlined which makes it possible to study Anderson localization in d > 2 dimensions.     

Effect of magnetic,crystal field and exchange interactions on graphene system: a Monte Carlo study

In this article, we employ the classical Monte Carlo approach to study the magnetic properties of graphene system. We analyze the ground-state phase diagrams in the presence of external magnetic and crystal fields under effect of the exchange interactions. The critical temperature is deduced. It is proven that the model exhibits the second-order phase transitions at the transition temperature. The total magnetization with the exchange interactions has studied under the temperatures effect. The total magnetization with the crystal field has been established under effect of exchange interactions and temperatures effect. The magnetic hysteresis cycles of graphene system is deduced under effect of temperatures and crystal field. The observations are in good agreement with related experiments and the other theoretical results. It is proven that the graphene system exhibits the superparamagnetic at the transition temperature and a specific value of reduced crystal field.     

Bi_2Sr_2CaCu_2O_8单晶中的反常尖锋效应

使用牛津震动样品磁强计 (VSM)研究了Bi2 Sr2 CaCu2 O8单晶的磁滞回线 .在 2 0到 40K温度之间发现了反常的尖锋效应 ,随样品O含量的增加 ,发生尖锋效应的外场也相应提高 .可以认为在尖峰效应处发生了由涡漩物质的有序固态到无序固态的相变 ,在有少量点缺陷存在的BSCCO单晶相图上 ,Bsp线终止于 2 0K温度处 ,在 2 0K以下温区没有发生准格子到涡漩玻璃的相变 ,涡漩固相始终以准格子形式存在 ;可以认为尖峰效应是外场、温度、无序的复杂函数     

The magnetic properties and anisotropy of the linear chain compound TlFe3Te3

The magnetic properties of TlFe₃Te₃ are studied on powdered samples and single crystals. Below 220 K TlFe₃Te₃, is a very anisotropic ferromagnet, the crystallographic c axis being the easy axis of magnetization. While in the easy direction saturation is achieved below 0.5 kOe, in the hard direction saturation is reached at 64 kOe. The angular dependence of the magnetization follows closely a cos ¦?¦ law. The magnetic transition is very abrupt at low external fields, suggesting a first order phase transition. It is accompanied by a small anomaly in the thermal dilatation of the c axis. The magnetization shows an anomalous increase below 50 K suggesting a phase transition.