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

Matthias Thamm1, Harini Radhakrishnan2,3, Hatem Barghathi2,3, C. M. Herdman4, Arpan Biswas5, Bernd Rosenow1, and Adrian Del Maestro2,3,6

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Phys. Rev. Lett. 135, 116002 – Published 11 September, 2025

DOI: https://doi.org/10.1103/4xdz-5vq7

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 renormalization group signatures, reconciling earlier discrepancies. Finally, leveraging a nonparametric Bayesian analysis, we determine the critical interaction strength with high precision to be Uc/J=3.275(2), establishing a benchmark for BKT physics in one-dimensional quantum models.

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Phys. Rev. Lett. 135, 116002– Published 11 September, 2025
  • Received 10 March 2025
  • Revised 19 July 2025
  • Accepted 20 August 2025
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