# Quantum Electronic Circuit Simulation of Generalized sine-Gordon Models

## TL;DR

This paper proposes quantum simulators using superconducting circuits to study complex nonlinear quantum field theories, specifically the double sine-Gordon model, and analyzes its thermodynamic properties and quantum integrability.

## Contribution

It introduces a novel approach to simulate generalized sine-Gordon models with superconducting circuits and provides analytical and theoretical analysis of their thermodynamic behavior.

## Key findings

- Analytical computation of mass-spectrum and ground state energy.
- Derivation of thermodynamic Bethe ansatz equations.
- Proposal of experiments to verify quantum integrability.

## Abstract

Investigation of strongly interacting, nonlinear quantum field theories (QFT-s) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFT-s using mesoscopic superconducting circuit lattices. Using the Josephson effect as the source of nonlinear interaction, we investigate generalizations of the quantum sine-Gordon model. In particular, we consider a two-field generalization, the double sine-Gordon model. In contrast to the sine-Gordon model, this model can be purely quantum integrable, when it does not admit a semi-classical description - a property that is generic to many multi-field QFT-s. The primary goal of this work is to investigate different thermodynamic properties of the double sine-Gordon model and propose experiments that can capture its subtle quantum integrability. First, we analytically compute the mass-spectrum and the ground state energy in the presence of an external `magnetic' field using Bethe ansatz and conformal perturbation theory. Second, we calculate the thermodynamic Bethe ansatz equations for the model and analyze its finite temperature properties. Third, we propose experiments to verify the theoretical predictions.