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arXiv:2107.08238 · Physical review. B./Physical review. B

Stark many-body localization transitions in superconducting circuits

Yong-Yi Wang, Zheng‐Hang Sun, Heng Fan

Published Nov 19, 2021• 24 citations
arXivHTMLPDF

Abstract

Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjected to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the one-dimensional array of superconducting qubits, and the circuit where nonlocal interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly excited eigenstates, and study the nonequilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay ${t}^{\ensuremath{-}\ensuremath{\xi}}$. The exponent $\ensuremath{\xi}$ satisfies $\ensuremath{\xi}\ensuremath{\propto}|\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\gamma}}_{c}{|}^{\ensuremath{\nu}}$ when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}$, and vanishes for $\ensuremath{\gamma}\ensuremath{\ge}{\ensuremath{\gamma}}_{c}$, which can be employed to estimate the ${\ensuremath{\gamma}}_{c}$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.

DOI
10.1103/physrevb.104.205122

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In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.
Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight into the properties of Stark MBL and to discover unique entanglement characteristics specific to this phenomenon. The phase diagram analysis reveals different behavior with varying interaction strengths. Furthermore, we highlight the influence of domain wall structures on the breakdown of the entanglement entropy of the system. Moreover, the investigation of Out-of-Time-Ordered Correlator (OTOC) behavior demonstrates distinct responses to interactions based on domain wall configurations. Our findings contribute to a better understanding of Stark MBL and offer valuable insights into the entanglement properties of systems subjected to Stark potentials.
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.
Utilizing exact diagonalization techniques, we investigate a one-dimensional, nonreciprocal, interacting hard-core boson model under a Stark potential with tail curvature. By employing the nonzero imaginary eigenenergies ratio, half-chain entanglement entropy, and eigenstate instability, we numerically confirm that the critical points of spectral real-complex (RC) transition and many-body localization (MBL) phase transition are not identical, and an examination of the phase diagrams reveals that the spectral RC transition arises before the MBL phase transition, which suggests the existence of a non-MBL-driven spectral RC transition. These findings are quite unexpected, and they are entirely different from observations in disorder-driven interacting non-Hermitian systems. This work provides a useful reference for further research on phase transitions in disorder-free interacting non-Hermitian systems.