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

摘要: 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 using gap extrapolation procedures is usually challenging and inaccurate due exponentially small value vicinity point, we show that a generic analysis, including effects logarithmic corrections, provides very accurate estimates BKT transition variety spin fermionic models. As first example, scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well nonintegrable spin-$3/2$ XXZ model, which known exhibit strong finite-size effects. then analyze extended Hubbard whose has been debated, finding results are consistent previous studies based on Luttinger-liquid parameter. Finally, investigate an anisotropic for present line large-scale simulations. Our work demonstrates analyses can help efficiently points, without relying model-dependent assumptions.