Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator

TL;DR

This paper computes dynamical correlation functions in the one-dimensional Bose-Hubbard insulator using strong-coupling expansion and DMRG, revealing their behavior near the Mott transition with good cross-method agreement.

Contribution

It provides a detailed calculation of dynamical correlation functions using multiple methods, extending understanding of the Bose-Hubbard model near the Mott insulator phase.

Findings

Correlation functions are finite above the single-particle gap with a square-root onset.

Features of the Hubbard bands are observed in the correlation functions.

Excellent agreement between strong-coupling expansion and DMRG results.

Abstract

We calculate the dynamical current and kinetic-energy correlation functions for the first Mott lobe of the one-dimensional Bose-Hubbard model. We employ the strong-coupling expansion up to sixth order in $x=t/U$, and the dynamical density-matrix renormalization group method on rings with 64 sites. The correlation functions are finite above the single-particle gap with a square-root onset, as is also found from field theory close to the Mott transition. The correlation functions display a featureless superposition of the primary and tertiary Hubbard bands. We find very good agreement between all methods in the interaction/frequency regimes where they are applicable.