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 β and/or large lattice size L, while they are in good agreement in the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit to keep 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 and implies that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.
Highlights
In this article, we consider the same one-dimensional Thirring model at finite density and perform Monte Carlo simulations taking the most dominant thimble with the hybrid Monte Carlo (HMC) algorithm proposed in ref. [51]
We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble
We consider the same one-dimensional Thirring model at finite density and perform Monte Carlo simulations taking the most dominant thimble with the HMC algorithm proposed in ref
Summary
The one-dimensional lattice Thirring model we consider in this paper is defined by the following action [21, 22, 65,66,67], L. The μ-dependence of these observables are plotted in figure 1 for L = 8, ma = 1, and β = 1, 3, 6 It shows a crossover behavior in the chemical potential μ (in the lattice unit) around μ ≃ m + ln(I0(β)/I1(β)). The continuum limits of n and χχ are obtained as follows: lim n a→0 lim χχ a→0 From these results, one can see that the model shows a crossover behavior in the chemical potential μ for a non-zero temperature T > 0, while in the zero temperature limit T = 0, it shows a first-order transition at the critical chemical potential μc = m + g2.
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