Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExperimental characterization of quantum many-body localization transition
127
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of a $N=12$ superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with different spatial resolution, we identify the transition point with excellent match between simulation and experiment. In addition, one can detect the evidence of mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.
rate research
Read More
While many-body localization (MBL) is a well-established phenomenon in one-dimension, the fate of higher-dimensional strongly disordered systems in the infinite-time limit is a topic of current debate. The latest experiments as well as several recent numerical studies indicate that such systems behave many-body localized -- at least on practically relevant time scales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL-to-thermal transition points, an important requirement to demonstrate their validity. Here, we develop a formalism to apply fermionic quantum circuits combined with automatic differentiation to simulate two-dimensional MBL systems realized in optical lattice experiments with fermions. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. We argue that our approach best captures the underlying charge-density-wave experiments and calculate other quantities which can be compared to future experiments, such as the mean localization lengths.
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.
A key feature of the many-body localized phase is the breaking of ergodicity and consequently the emergence of local memory; revealed as the local preservation of information over time. As memory is necessarily a time dependent concept, it has been partially captured by a few extant studies of dynamical quantities. However, these quantities are neither optimal, nor democratic with respect to input state; and as such a fundamental and complete information theoretic understanding of local memory in the context of many-body localization remains elusive. We introduce the dynamical Holevo quantity as the true quantifier of local memory, outlining its advantages over other quantities such as the imbalance or entanglement entropy. We find clear scaling behavior in its steady-state across the many-body localization transition, and determine a family of two-parameter scaling ansatze which captures this behavior. We perform a comprehensive finite size scaling analysis of this dynamical quantity extracting the transition point and scaling exponents.
We investigate the occurrence of the phenomenon of many-body localization (MBL) on a D-Wave 2000Q programmable quantum annealer. We study a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph, with random exchange interactions and random longitudinal fields. On this system we experimentally observe a transition from an ergodic phase to an MBL phase. We first theoretically show that the MBL transition is induced by a critical disorder strength for individual energy eigenstates in a Chimera cell, which follows from the analysis of the mean half-system block entanglement, as measured by the von Neumann entropy. We show the existence of an area law for the block entanglement over energy eigenstates for the MBL phase, which stands in contrast with an extensive volume scaling in the ergodic phase. The identification of the MBL critical point is performed via the measurement of the maximum variance of the mean block entanglement over the disorder ensemble as a function of the disorder strength. Our results for the energy density phase diagram also show the existence of a many-body mobility edge in the energy spectrum. The time-independent disordered Ising Hamiltonian is then experimentally realized by applying the reverse annealing technique allied with a pause-quench protocol on the D-Wave device. We then characterize the MBL critical point through magnetization measurements at the end of the annealing dynamics, obtaining results compatible with our theoretical predictions for the MBL transition.
We propose a new approach to probing ergodicity and its breakdown in quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the systems eigenstates, finding a qualitatively different behaviour in the many-body localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter ${cal G}(L)=langle ln (V_{nm}/delta) rangle$, which represents a disorder-averaged ratio of a typical matrix element of a local operator $V$ to the energy level spacing, $delta$; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter ${cal G}(L)$ decreases with system size $L$ in the MBL phase, and grows in the ergodic phase. We surmise that the delocalization transition occurs when ${cal G}(L)$ is independent of system size, ${cal G}(L)={cal G}_csim 1$. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered 1D XXZ spin-1/2 chain using exact diagonalization and time-evolving block decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular logarithmically slow transport at the transition, and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization group predictions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
