# Phase structure of the 1+1 dimensional massive Thirring model from matrix product states

## TL;DR

This study uses matrix product states to explore the phase diagram of the (1+1)-dimensional massive Thirring model, revealing critical and gapped phases separated by a BKT transition, and demonstrating the method's effectiveness in quantum field theory.

## Contribution

The paper introduces a novel application of matrix product states to analyze the phase structure of the massive Thirring model, including the identification of a BKT transition.

## Key findings

- Identified critical and gapped phases in the model.
- Provided numerical evidence of a BKT phase transition.
- Showed the model can be conformal with non-zero fermion mass.

## Abstract

Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model.