Loschmidt echo singularities as dynamical signatures of strongly localized phases

TL;DR

This paper reveals that strongly localized phases exhibit universal cusp singularities in the Loschmidt echo after a quantum quench, providing a new experimental signature of localization and interactions in quantum systems.

Contribution

It demonstrates that Loschmidt echo singularities serve as a universal dynamical signature of localized phases, including interacting ones, accessible to current quantum simulators.

Findings

Universal cusp singularities in Loschmidt echo observed

Simple Rabi oscillation model captures key dynamics

Faster decay of singularities indicates interactions

Abstract

Quantum localization (single-body or many-body) comes with the emergence of local conserved quantities -- whose conservation is precisely at the heart of the absence of transport through the system. In the case of fermionic systems and $S=1/2$ spin models, such conserved quantities take the form of effective two-level systems, called $l$-bits. While their existence is the defining feature of localized phases, their direct experimental observation remains elusive. Here we show that strongly localized $l$-bits bear a dramatic universal signature, accessible to state-of-the-art quantum simulators, in the form of periodic cusp singularities in the Loschmidt echo following a quantum quench from a N\'eel/charge-density-wave state. Such singularities are perfectly captured by a simple model of Rabi oscillations of an ensemble of independent two-level systems, which also reproduces the short-time behavior of the entanglement entropy and the imbalance dynamics. In the case of interacting localized phases, the dynamics at longer times shows a sharp crossover to a faster decay of the Loschmidt echo singularities, offering an experimentally accessible signature of the interactions between $l$-bits.