Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

TL;DR

This study investigates the Lefschetz thimble structure of the one-dimensional Thirring model at finite density, revealing the importance of subdominant thimbles for accurately capturing phase transitions, especially at low temperatures.

Contribution

It provides the first numerical analysis of the Thirring model's thimble structure, highlighting the need to include subdominant thimbles for correct phase transition representation.

Findings

Discrepancy between numerical and exact results in crossover region at small β and large L.

Good agreement at low and high density regions.

Discrepancy persists in the continuum limit and increases at low temperature.

Abstract

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $\beta$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.