Phase Diagram of the Schwinger Model by Adiabatic Preparation of States on a Quantum Simulator

TL;DR

This paper demonstrates a novel adiabatic state preparation method to explore the phase diagram of the Schwinger model with a topological term on quantum simulators, revealing phase transition regions.

Contribution

It introduces a new adiabatic preparation technique for quantum states and applies it to study the phase structure of the Schwinger model with a topological term.

Findings

Successfully tested the method on the Schwinger model

Identified first-order and no-transition regions in the phase diagram

Compared advantages of the new method with existing approaches

Abstract

We argue the feasibility to study the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a novel method and successfully test it in application to the Schwinger model in the presence of a topological $\theta$-term. We explore the first-order-phase-transition and the no-transition regions of the corresponding phase diagram. The core idea of the method is to separately evolve the ground and the first excited states with a time-dependent Hamiltonian, the time-dependence of which interpolates between different values of $\theta$. Despite our approach being a direct application of the adiabatic theorem, in some cases we are able to demonstrate its advantages in comparison to a different method from the literature that also employs adiabatic state preparation.