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Bose-Hubbard Model with Power-Law Hopping in One Dimension.

Tanul Gupta1, Nikolay V Prokof'ev2, Guido Pupillo1

  • 1University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France.

Physical Review Letters
|May 29, 2026
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Summary
This summary is machine-generated.

This study reveals distinct quantum phase transitions in long-range Bose-Hubbard models. For hopping exponents 1<α≤3, transitions are continuous, unlike the BKT scenario for α>3.

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Area of Science:

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

Background:

  • The Bose-Hubbard model describes interacting bosons on a lattice.
  • Power-law hopping introduces long-range interactions, deviating from standard models.
  • Understanding quantum phase transitions is crucial for novel materials and quantum computing.

Purpose of the Study:

  • Investigate the zero-temperature phase diagram of the 1D Bose-Hubbard model with power-law hopping (1/r^α).
  • Characterize quantum phase transitions between superfluid and Mott insulator phases.
  • Determine the universality classes and ordering regimes in the long-range regime.

Main Methods:

  • Exact large-scale quantum Monte Carlo simulations.
  • Finite-size scaling analysis of superfluid stiffness.
  • Extraction of dynamical and correlation-length exponents from the low-energy spectrum.

Main Results:

  • Continuous, scale-invariant quantum phase transitions for 1<α≤3, distinct from the BKT scenario (α>3).
  • Identification of a new universality class for long-range quantum phase transitions (1<α≤3).
  • Revealed ordering regimes: true long-range order (α≤2), anomalous quasi-long-range order (2<α≤3), and algebraic decay (α>3).

Conclusions:

  • The long-range Bose-Hubbard model exhibits unique quantum phase transitions and ordering phenomena.
  • Numerical results provide benchmarks for theories of long-range quantum systems.
  • Findings are relevant for experiments involving cold atoms, molecules, and ion chains.