Phase Transitions in One-Dimensional Truncated Bosonic Hubbard Model and Its Spin-1 Analog

TL;DR

This paper investigates phase transitions in a one-dimensional truncated bosonic Hubbard model and its spin-1 analog, revealing unique critical behaviors and phase boundaries through exact numerical methods.

Contribution

It provides the first detailed analysis of phase transitions in the truncated bosonic Hubbard model and connects these findings to a spin-1 model with axial anisotropy.

Findings

Mott-insulator to superfluid transition occurs at (U/t)_c=0.50±0.05, differing from the full model.

Identifies a transition from one-particle to two-particle superfluid in the attractive regime.

Two-particle superfluid exhibits a linear pairing gap near the critical point.

Abstract

We study one-dimensional truncated (no more than 2 particles on a site) bosonic Hubbard model in both repulsive and attractive regimes by exact diagonalization and exact worldline Monte Carlo simulation. In the commensurate case (one particle per site) we demonstrate that the point of Mott-insulator -- superfluid transition, $(U/t)_c=0.50\pm 0.05$, is remarkably far from that of the full model. In the attractive region we observe the phase transition from one-particle superfluid to two-particle one. The paring gap demonstrates a linear behavior in the vicinity of the critical point. The critical state features marginal response to the gauge phase. We argue that the two-particle superfluid is a macroscopic analog of a peculiar phase observed earlier in a spin-1 model with axial anisotropy.