Renormalization group analysis of $p$-orbital Bose-Einstein condensates in a square optical lattice

TL;DR

This paper uses Wilsonian renormalization group analysis to study quantum fluctuations in $p$-orbital Bose-Einstein condensates in a square optical lattice, revealing how fluctuations influence phase boundaries and induce order.

Contribution

It provides the first renormalization group analysis of $p$-orbital BECs, showing quantum fluctuations can induce order without destroying it, unlike in $s$-orbital systems.

Findings

Quantum fluctuations induce ordered phases in $p$-orbital BECs.

Renormalization group corrections modify phase boundaries.

Quantum fluctuations do not destroy but promote order via Coleman-Weinberg mechanism.

Abstract

We investigate the quantum fluctuation effects in the vicinity of the critical point of a $p$-orbital bosonic system in a square optical lattice using Wilsonian renormalization group, where the $p$-orbital bosons condense at nonzero momenta and display rich phases including both time-reversal symmetry invariant and broken BEC states. The one-loop renormalization group analysis generates corrections to the mean-field phase boundaries. We also show the quantum fluctuations in the $p$-orbital system tend to induce the ordered phase but not destroy it via the the Coleman-Weinberg mechanism, which is qualitative different from the ordinary quantum fluctuation corrections to the mean-field phase boundaries in $s$-orbital systems. Finally we discuss the observation of these phenomena in the realistic experiment.