Stark many-body localization transitions in superconducting circuits

TL;DR

This paper investigates the Stark many-body localization transition in superconducting circuits, analyzing entanglement, participation entropy, and non-equilibrium dynamics to identify critical behavior and demonstrate the platform's suitability for studying MBL phenomena.

Contribution

It provides the first detailed analysis of Stark MBL in superconducting circuits, including critical point estimation and non-equilibrium relaxation properties.

Findings

Identification of the critical linear potential $oldsymbol{oldsymbol{ extgamma}_c}$ for Stark MBL.

Observation of power-law decay in imbalance relaxation near the transition.

Superconducting circuits are shown to be a promising platform for studying MBL transitions.

Abstract

Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjecting 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 1D array of superconducting qubits, and the circuit where non-local interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly-excited eigenstates, and obtain the lower bound of the critical linear potential $\gamma_{c}$, using the finite-size scaling collapse. Moreover, we study the non-equilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay $t^{-\xi}$. The exponent $\xi$ satisfies $\xi\propto|\gamma-\gamma_{c}|^{\nu}$ when $\gamma<\gamma_{c}$, and vanishes for $\gamma\geq \gamma_{c}$, which can be employed to estimate the $\gamma_{c}$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.