Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps

TL;DR

This paper explores the equilibrium and dynamical behavior of the Bose-Hubbard model near the superfluid to Mott insulator transition, identifying universal scaling laws during slow ramps.

Contribution

It provides a comprehensive comparison of multiple computational methods and characterizes the universal dynamics during slow parameter ramps across the phase transition.

Findings

Benchmarking of methods for equilibrium properties

Identification of universal power law scaling in slow ramps

Estimation of optimal protocols for observing scaling

Abstract

We investigate the equilibrium and dynamical properties of the Bose-Hubbard model and the related particle-hole symmetric spin-1 model in the vicinity of the superfluid to Mott insulator quantum phase transition. We employ the following methods: exact-diagonalization, mean field (Gutzwiller), cluster mean-field, and mean-field plus Gaussian fluctuations. In the first part of the paper we benchmark the four methods by analyzing the equilibrium problem and give numerical estimates for observables such as the density of double occupancies and their correlation function. In the second part, we study parametric ramps from the superfluid to the Mott insulator and map out the crossover from the regime of fast ramps, which is dominated by local physics, to the regime of slow ramps with a characteristic universal power law scaling, which is dominated by long wavelength excitations. We calculate values of several relevant physical observables, characteristic time scales, and an optimal protocol needed for observing universal scaling.