Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition

TL;DR

This study uses advanced numerical methods to analyze the BKT transition in the 1D Bose-Hubbard model, revealing universal scaling behavior and precisely determining the critical point.

Contribution

It provides a systematic finite-size scaling approach and Bayesian analysis to accurately identify BKT transition signatures in a quantum model.

Findings

Confirmed logarithmic finite-size scaling of BKT transition

Reconciled boundary effects with universal RG signatures

Precisely determined the critical interaction strength

Abstract

We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT transition. Employing density matrix renormalization group and quantum Monte Carlo simulations under periodic boundary conditions, together with a systematic finite-size scaling analysis of bipartite particle number fluctuations, we resolve boundary-induced complications that previously obscured critical scaling. We demonstrate that a suitably chosen central region under open boundaries reproduces universal RG signatures, reconciling earlier discrepancies. Finally, leveraging a non-parametric Bayesian analysis, we determine the critical interaction strength with high precision, establishing a benchmark for BKT physics in one-dimensional quantum models.