Real-Time Ginzburg-Landau Theory for Bosons in Optical Lattices

TL;DR

This paper develops a real-time Ginzburg-Landau theory for the Bose-Hubbard model using the Schwinger-Keldysh formalism, capturing excitation dynamics near quantum phase transitions and aligning with experimental observations.

Contribution

It introduces a novel real-time Ginzburg-Landau framework for bosons in optical lattices, linking excitations across phases and matching experimental spectra.

Findings

Particle/hole dispersions map continuously across phases

Identifies a sound mode consistent with Bragg spectroscopy

Detects a gapped mode observed in lattice modulation experiments

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 transitions it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase. Furthermore, in the superfluid phase we find a sound mode, which is in accordance with recent Bragg spectroscopy measurements in the Bogoliubov regime, as well as an additional gapped mode, which seems to have been detected via lattice modulation.