Gaussian quantum fluctuations in the superfluid-Mott phase transition

TL;DR

This paper derives the elementary excitations of the superfluid-Mott transition in bosonic systems, showing that Gaussian quantum fluctuations can change the transition's nature from second-order to first-order, providing a benchmark for future experiments.

Contribution

It provides a theoretical derivation of excitation spectra and analytical formulas for the equation of state, highlighting the impact of quantum fluctuations on the phase transition order.

Findings

Energy spectrum matches experimental data

Quantum fluctuations can induce first-order transition

Analytical formulas for equations of state in 2D and 3D

Abstract

Recent advances in cooling techniques make now possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gappless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for next future experiments on quantum phase transitions.