Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models

TL;DR

This paper demonstrates that gap-scaling analysis, including logarithmic corrections, can accurately locate Berezinskii-Kosterlitz-Thouless (BKT) critical points in various quantum models, overcoming challenges of traditional methods.

Contribution

It introduces a generic gap-scaling approach with logarithmic corrections for precise BKT transition detection in spin and fermionic models.

Findings

Effective in non-integrable spin-$3/2$ XXZ model with finite-size effects

Consistent results for BKT transition in extended Hubbard model

First estimates of BKT line in anisotropic extended Hubbard model

Abstract

We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universality class by means of gap-scaling analyses. While accurately determining such points using gap extrapolation procedures is usually challenging and inaccurate due to the exponentially small value of the gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, including the effects of logarithmic corrections, provides very accurate estimates of BKT transition points in a variety of spin and fermionic models. As a first example, we show how the scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well in a non-integrable spin-$3/2$ XXZ model, which is known to exhibit strong finite-size effects. We then analyze the extended Hubbard model, whose BKT transition has been debated, finding results that are consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally, we investigate an anisotropic extended Hubbard model, for which we present the first estimates of the BKT transition line based on large-scale density-matrix-renormalization-group simulations. Our work demonstrates how gap-scaling analyses can help to locate accurately and efficiently BKT critical points, without relying on model-dependent scaling assumptions.