Time dependent mean field theory of the superfluid-insulator phase transition

TL;DR

This paper introduces a time-dependent mean field approach to analyze the superfluid-insulator phase transition, providing phase diagrams for the Bose-Hubbard and spin-S Heisenberg models that align with existing numerical and perturbative results.

Contribution

The authors develop a novel time-dependent mean field method to study quantum phase transitions, deriving phase diagrams for the Bose-Hubbard and Heisenberg models with improved accuracy.

Findings

Phase diagrams show lobe-like structures for both models.

The approach matches Quantum Monte Carlo and perturbative results.

Derived phase boundaries relate the Bose-Hubbard and Heisenberg models.

Abstract

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.