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arXiv:2002.07635 · Physical Review Letters

Slow Many-Body Delocalization beyond One Dimension

Elmer V. H. Doggen, I. V. Gornyi, A. D. Mirlin, Dmitry G. Polyakov

Published Oct 5, 2020• 57 citations
arXivHTMLPDF

Abstract

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and timescales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder W_{c}(L,d) as a function of length L and width d. In the quasi-1D case W_{c} has a finite large-L limit at fixed d, which increases strongly with d. In the 2D case W_{c}(L,L) grows with L. The results are consistent with the avalanche picture of the many-body localization transition.

DOI
10.1103/physrevlett.125.155701

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We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and timescales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder W_{c}(L,d) as a function of length L and width d. In the quasi-1D case W_{c} has a finite large-L limit at fixed d, which increases strongly with d. In the 2D case W_{c}(L,L) grows with L. The results are consistent with the avalanche picture of the many-body localization transition.
We use thermalization indicators and numerical linked cluster expansions to probe the onset of many-body localization in a disordered one-dimensional hard-core boson model in the thermodynamic limit. We show that after equilibration following a quench from a delocalized state, the momentum distribution indicates a freezing of one-particle correlations at higher values than in thermal equilibrium. The position of the delocalization to localization transition, identified by the breakdown of thermalization with increasing disorder strength, is found to be consistent with the value from the level statistics obtained via full exact diagonalization of finite chains. Our results strongly support the existence of a many-body localized phase in the thermodynamic limit.
We use thermalization indicators and numerical linked cluster expansions to probe the onset of many-body localization in a disordered one-dimensional hard-core boson model in the thermodynamic limit. We show that after equilibration following a quench from a delocalized state, the momentum distribution indicates a freezing of one-particle correlations at higher values than in thermal equilibrium. The position of the delocalization to localization transition, identified by the breakdown of thermalization with increasing disorder strength, is found to be consistent with the value from the level statistics obtained via full exact diagonalization of finite chains. Our results strongly support the existence of a many-body localized phase in the thermodynamic limit.
We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the many-body localization transition by using single-particle Anderson localization on the Bethe lattice as a toy model of many-body dynamics in Fock space. We probe the dynamical evolution by measuring observables such as the imbalance and equilibrium correlation functions, which display slow dynamics and power laws strikingly similar to those observed in recent simulations and experiments. We relate this unusual behavior to the nonergodic spectral statistics found on Bethe lattices. We discuss different scenarios, such as a true intermediate phase which persists in the thermodynamic limit versus a glassy regime established on finite but very large time and length scales only, and their implications for real-space dynamical properties. In the latter, slow dynamics and power laws extend on a very large time window but are eventually cut off on a time scale that diverges at the many-body localization transition.
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We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times $(\ensuremath{\sim}{10}^{4})$ and find a universal behavior of the spectral function.
Quantum many-body systems with sufficiently strong disorder can exhibit a non-equilibrium phenomenon, known as the many-body localization (MBL), which is distinct from conventional thermalization. While the MBL regime has been extensively studied in one dimension, its existence in higher dimensions remains elusive, challenged by the avalanche instability. Here, using a 70-qubit two-dimensional (2D) superconducting quantum simulator, we experimentally explore the robustness of the MBL regime in controlled finite-size 2D systems. We observe that the decay of imbalance becomes more pronounced with increasing system sizes, scaling up from 21, 42 to 70 qubits, with a relatively large disorder strength, and for the first time, provide an evidence for the many-body delocalization in 2D disordered systems. Our experimental results are consistent with the avalanche theory that predicts the instability of MBL regime beyond one spatial dimension. This work establishes a scalable platform for probing high-dimensional non-equilibrium phases of matter and their finite-size effects using superconducting quantum circuits.