The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.
It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localizat…
We study the dynamics of the quenched Anderson model at finite temperature using matrix product states. Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearest-neighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes -- possible when simulating the ful…
A metal can be driven to an insulating phase through distinct mechanisms. A possible way is via the Coulomb interaction, which then defines the Mott metal-insulator transition (MIT). Another possibility is the MIT driven by disorder, the so-called Anderson MIT. Here we analyze interacting particles in disordered Hubbard chains $-$ thus comprising the Mott-Anderson physics $-$ by investigating the ground-state entanglement with density functional theory. The localization signature on entanglement is found to be a local minimum at a certain critical density. Individually, the Mott (Anderson) MIT…
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space periodic potentials, crystalline phenomena in time can be modelled by periodically driven systems. Disorder in the periodic driving can lead to Anderson localization in time: the probability for detecting a system at a fixed point of configuration space becomes exponentially localized around a certain moment in time. We here show that a three-dimensional system e…
We study the ground-state entanglement entropy of a subsystem of size $L$ of non-interacting fermions scattered by a potential of finite range $a$. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove, that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies and the full counting statistics are robust against potential scattering, provided that $L/a\gg 1$. The results of numerical calculations support the validity of this conclusion for a generic potential.
The Anderson model with decoherence features a temporal evolution from localized eigenstates to a uniform spatial distribution bar any interference features. We discuss the growth and decay of pronounced interference peaks on transient time-scales and develop an analytic understanding for the emergence of these peaks.
The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. Here we study the localization transition in the prototypical three-dimensional, noninteracting Anderson model when the system is driven at its boundaries to induce a current carrying non-equilibrium steady state. Recently we showed that the diffusive phase of this model exhibits extensive mutual information of its non-equilibrium steady-state densi…
Experimental realization of the complete seven-phase Anderson-localization landscape
Department of Physics and State Key Laboratory of Quantum Functional Materials, Southern University of Science and Technology（南方科技大学物理系与量子功能材料国家重点实验室）；Shenzhen Institute for Quantum Science and Engineering and Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学深圳量子科学与工程研究院与广东省量子科学与工程重点实验室）
We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest model of a 1D disordered chain and we analyse both the dynamics of an initially localized state and the dynamics of quantum states drawn at random from the ensemble corresponding to the minimum knowledge about the initial state. While in the former case the site distribution remains confined in a limited portion of the chain, the site distribution of random p…
In this paper, we present a general correspondence between the mosaic and non-mosaic models, which can be used to obtain the exact solution for the mosaic ones. This relation holds not only for the quasicrystal models, but also for the Anderson models. Despite the different localization properties of the specific models, this relationship shares a unified form. Applying our method to the mosaic Anderson models, we find that there is a discrete set of extended states. At last, we also give the general analytical mobility edge for the mosaic slowly varying potential models and the mosaic Ganesha…
We investigate the Mott-Anderson physics in interacting disordered one-dimensional chains through the average single-site entanglement quantified by the linear entropy, which is obtained via density-functional theory calculations. We show that the minimum disorder strength required to the so-called full Anderson localization $-$ characterized by the real-space localization of pairs $-$ is strongly dependent on the interaction regime. The degree of localization is found to be intrinsically related to the interplay between the correlations and the disorder potential. In magnetized systems, the m…
Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently, the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. N…
Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor -- equivalent to a two-dimensional Anderson-like model -- we experimentally study Anderson localization in dimension 2 and we observe localized wavefunction dynamics. We also show that the localization length depends exponentially on the disorder strength and anisotropy and is in quantitative agreement with the predictions of the self-consistent theory for the 2D Anderson localization.
We study the effects of acceleration on fermionic Gaussian states of localized modes of a Dirac field. We consider two wave-packets in a Gaussian state and transform these to an accelerated frame of reference. In particular, we formulate the action of this transformation as a fermionic quantum channel. Having developed the general framework for fermions, we then investigate the entanglement of the vacuum, as well as the entanglement in Bell states. We find that with increasing acceleration vacuum entanglement increases, while the entanglement of Bell states decreases. Notably, our results have…
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum suppression of classical diffusion in systems that are classically chaotic. Another kind of Anderson localization has been recently proposed, i.e. localization in the time domain due to the presence of {\it disorder} in time. That is, the probability density for the detection of a system at a fixed position in the configuration space is localized exponentially ar…
We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions driven by the quasiperiodic disorder. Unlike the gapless and localized TAI phase in one-dimensional random disordered systems, we …
We experimentally study the effects of coupling one-dimensional Many-Body Localized (MBL) systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artifically prepare an initial charge density wave in an array of 1D tubes with quasi-random onsite disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between MBL and Anderson Localization. While the non-interacting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire …
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase which is ergodic at large scales but strongly non-ergodic at smaller scales. In the critical regime, multifractal wavefunctions are located on few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusua…
In models of hopping disorder in the absence of external fields and at the band center, the electrons are less localized in space than the standard exponential Anderson localization. A signature of this anomalous localization is the square root dependence of the logarithmic average of the conductance on the system length, in contrast to the linear length dependence for Anderson localized systems. We study the effect of a time-periodic external field in the scaling and distribution of the conductance of a quantum wire with hopping disorder. In the low-frequency regime, we show a transition betw…
Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermaliza…
