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arXiv:2511.14260 · Physical Review A

Stability of current-carrying states in hard-core bosons with long-range hopping on a square lattice

Yoshihiro Yabuuchi, Ippei Danshita

Published May 19, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the stability of current-carrying states with quasi-momentum $K$ in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance $r$ with hopping amplitude decaying algebraically with $r$ as $\propto r^{-α}$. Using a mean-field theory, we analyze the excitation spectrum and determine the critical quasi-momenta associated with Landau and dynamical instabilities. We find that the long-range hopping suppresses the critical quasi-momenta and makes them vanish at $α=3$. Near $α=3$, we show that the critical quasi-momentum $K_{\mathrm{c}}$ for the dynamical instability exhibits the scaling behavior $K_\mathrm{c} \propto Δ^{1+Δ}$ with $Δ=α-3$, where the scaling exponent explicitly depends on $Δ$, as a consequence of the long-range nature of the hopping.

DOI
10.1103/xvx2-n5j2

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We investigate the stability of current-carrying states with quasi-momentum KKK in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance rrr with hopping amplitude decaying algebraically with rrr as ∝r−α\propto r^{-α}∝r−α. Using a mean-field theory, we analyze the excitation spectrum and determine the critical quasi-momenta associated with Landau and dynamical instabilities. We find that the long-range hopping suppresses the critical quasi-momenta and makes them vanish at α=3α=3α=3. Near α=3α=3α=3, we show that the critical quasi-momentum KcK_{\mathrm{c}}Kc​ for the dynamical instability exhibits the scaling behavior Kc∝Δ1+ΔK_\mathrm{c} \propto Δ^{1+Δ}Kc​∝Δ1+Δ with Δ=α−3Δ=α-3Δ=α−3, where the scaling exponent explicitly depends on ΔΔΔ, as a consequence of the long-range nature of the hopping.
The two-dimensional square lattice hard-core boson Hubbard model with near-neighbor interactions has a ``checkerboard'' charge density wave insulating phase at half filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long-range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near-neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions, we conclude that phase separation still occurs.
We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for noninteracting hard-core bosons the effective attraction induced by the correlated hopping leads to phase separation at low density, we show that a modest nearest-neighbor repulsion suppresses phase separation, leading to a remarkable low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signaling a condensation of pairs. We also explain why the unusual properties of the pairing phase are a real challenge for standard one-worm quantum Monte Carlo simulations.
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We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15z=0.15z=0.15, which is smaller than results obtained on smaller lattices. This indicates that zzz approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.
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