Probing the superfluid-insulator phase transition by a non-Hermitian external field

TL;DR

This paper investigates how a non-Hermitian external field can be used to detect the superfluid-insulator quantum phase transition in Hubbard-like systems by analyzing the system's dynamical response and fidelity decay.

Contribution

It introduces a novel method using non-Hermitian perturbations to probe quantum phase transitions, focusing on the superfluid-insulator transition in finite-size models.

Findings

Uhlmann fidelity decay distinguishes phases at zero temperature.

Exceptional point dynamics relate to fluctuations in boson and polariton numbers.

Method applies to models like Bose-Hubbard and Jaynes-Cummings-Hubbard.

Abstract

We study the response of a thermal state of the Hubbard-like system to either global or local non-Hermitian perturbation, which coalesces the degenerate ground state within the $U(1)$ symmetry breaking phase. We show that the dynamical response of the system is strongly sensitive to the underlying quantum phase transition (QPT) from a Mott insulator to a superfluid state. The Uhlmann fidelity in the superfluid phase decays to a steady value determined by the order of the exceptional point (EP) within the subspace spanned by the degenerate ground states but remains almost unchanged in the Mott insulating phase. It demonstrates that the phase diagram at zero temperature is preserved even though a local probing field is applied. Specifically, two celebrated models including the Bose-Hubbard model and the Jaynes-Cummings-Hubbard model are employed to demonstrate this property in the finite-size system, wherein fluctuations of the boson and polariton number are observed based on EP dynamics. This work presents an alternative approach to probe the superfluid-insulator QPT at non-zero temperature.