Excitation Spectra of Bosons in Optical Lattices from Schwinger-Keldysh Calculation

TL;DR

This paper develops a real-time Ginzburg-Landau theory for the Bose-Hubbard model using Schwinger-Keldysh formalism, revealing how excitations evolve across the quantum phase transition and aligning with recent experimental observations.

Contribution

It introduces a novel real-time theoretical framework for analyzing excitation spectra in the Bose-Hubbard model near the quantum phase transition.

Findings

Particle/hole dispersions in the Mott phase map onto amplitude/phase excitations in the superfluid phase

The theory predicts continuous evolution of excitations across the transition

Results align with recent Bragg spectroscopy measurements

Abstract

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transition it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase, which have been detected recently by Bragg spectroscopy measurements.