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arXiv:2108.08268 · Physical review. B./Physical review. B

Quantum circuits reproduce the experimental two-dimensional many-body localization transition point

Joey Li, Amos Chan, Thorsten B. Wahl

Published Apr 30, 2024• 3 citations
arXivHTMLPDF

Abstract

While many studies point towards the existence of many-body localization (MBL) in one dimension, the fate of higher-dimensional strongly disordered systems 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 timescales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL features---an important requirement to demonstrate their validity. In this Letter, we use fermionic quantum circuits as a variational method to approximate the full set of eigenstates of two-dimensional MBL systems realized in fermionic optical lattice experiments. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. Moreover, we calculate the filling-fraction-dependent MBL phase diagram. We argue that our approach best captures the underlying charge-density-wave experiments and compute the mean localization lengths, which can be compared to future experiments.

DOI
10.1103/physrevb.109.l140202

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While many studies point towards the existence of many-body localization (MBL) in one dimension, the fate of higher-dimensional strongly disordered systems 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 timescales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL features---an important requirement to demonstrate their validity. In this Letter, we use fermionic quantum circuits as a variational method to approximate the full set of eigenstates of two-dimensional MBL systems realized in fermionic optical lattice experiments. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. Moreover, we calculate the filling-fraction-dependent MBL phase diagram. We argue that our approach best captures the underlying charge-density-wave experiments and compute the mean localization lengths, which can be compared to future experiments.
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.
Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.
Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit the fact that localization of particles as realized in Anderson localization and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localization computed from the density distributions, the occupation distance, we systematically study its scaling behavior across delocalization transitions and identify critical points from scaling collapses of numerical data. Excellent agreement with literature results is found for the critical disorder strengths of noninteracting fermions, such as the one-dimensional Aubry-Andr\'e model and the three-dimensional Anderson model. We observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition. Finally, we use our measure to extract the transition point as a function of filling for interacting fermions.
We numerically investigate the effect of coupling a two-dimensional many-body localized system to a finite heat bath, using shallow quantum circuits as a variational ansatz. Specifically, we simulate optical lattice experiments with two components of ultracold bosons, where only one species is subject to a random disorder potential and the other acts as a heat bath. We obtain a filling fraction-dependent phase diagram with a critical filling consistent with experiments. We also perform long-time time-dependent variational principle (TDVP) simulations with matrix product states, but find that the quantum circuit approach produces superior results because of the lack of boundary effects. Finally, we present additional results on the two-point correlation functions and the quantum mutual information between sites.
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 study the many-body localization (MBL) transition in interacting fermionic systems on disordered one-dimensional lattices using a physics-informed machine-learning framework. Instead of feeding full many-body wave functions into the model, we construct a compact feature representation based on four physically motivated observables: the inverse participation ratio, the Shannon entropy, the many-body hybridization parameter, and the mean level-spacing ratio. These quantities capture complementary aspects of localization, entanglement, and spectral correlations, and are used to train a Kolmogorov--Arnold Network (KAN) classifier on eigenstates deep in the weak and strong disorder regimes. The resulting KAN achieves a validation accuracy exceeding 99.9%99.9\%99.9%, comparable to that of convolutional neural networks trained directly on high-dimensional wave-function data, while requiring substantially reduced input dimensionality and significantly shorter training time. Applying the trained classifier across the full energy spectrum yields energy-resolved phase diagrams that reveal a clear many-body mobility edge and provide a consistent estimate of the critical disorder strength. The approach is inherently extensible: additional physically relevant observables can be incorporated into the feature space in a systematic manner without altering the overall architecture. Our results demonstrate that feature-based learning with KAN provides an efficient, scalable, and interpretable methodology for identifying many-body localization transitions, offering a practical alternative to raw-data-based neural network approaches.