The massive Thirring / sine-Gordon model with non-zero current density

TL;DR

This paper calculates the zero-temperature equation of state for the massive Thirring / sine-Gordon model with non-zero current density, demonstrating bounds that are useful for Monte Carlo methods avoiding the sign problem.

Contribution

It applies recently derived bounds on the equation of state to the massive Thirring / sine-Gordon model using Bethe ansatz calculations, providing concrete energy density constraints.

Findings

Optimal bounds constrain energy density within a factor of two at high densities.

Lower bound becomes exact at low densities.

Upper bound approaches a factor of 4.90 constraint.

Abstract

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a non-zero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring / sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90.