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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Statistical Mechanics

Background:

  • The Berezinskii-Kosterlitz-Thouless (BKT) transition is a fundamental concept in low-dimensional quantum systems.
  • Previous studies faced challenges in observing universal BKT scaling due to boundary effects in numerical simulations.
  • The one-dimensional Bose-Hubbard model provides a crucial platform for investigating quantum phase transitions.

Purpose of the Study:

  • To provide definitive numerical evidence for the BKT transition in the 1D Bose-Hubbard model at unit filling.
  • To resolve discrepancies in critical scaling observed in prior numerical investigations.
  • To establish a precise benchmark for the critical interaction strength in this model.

Main Methods:

  • Utilizing density matrix renormalization group (DMRG) and quantum Monte Carlo (QMC) simulations.
  • Applying periodic and open boundary conditions to analyze finite-size scaling.
  • Employing systematic analysis of bipartite particle number fluctuations.
  • Leveraging nonparametric Bayesian analysis for precise parameter determination.

Main Results:

  • Observed characteristic logarithmic finite-size scaling, confirming the BKT transition.
  • Demonstrated that a central region under open boundaries reveals universal renormalization group signatures.
  • Reconciled earlier discrepancies by addressing boundary-induced complications.
  • Determined the critical interaction strength U_c/J with high precision: 3.275(2).

Conclusions:

  • The study successfully resolves boundary effects obscuring BKT critical scaling in 1D quantum models.
  • A precise critical interaction strength benchmark is established for the 1D Bose-Hubbard model.
  • The findings provide robust evidence and a reliable method for studying BKT physics in similar systems.