Frustration effects in rapidly rotating square and triangular optical lattices

TL;DR

This paper analyzes the ground state phase diagram of rotating Bose-Hubbard models on square and triangular lattices, revealing how frustration and lattice topology influence phase transitions and stability.

Contribution

It introduces a non-perturbative quantum rotor approach with topological constraints to derive an improved phase diagram for rotating Bose-Hubbard systems.

Findings

Maximum repulsive energy derived for specific frustration parameters

Triangular lattice states are most stable against rotation effects

Critical ratio of kinetic to on-site energy depends on lattice topology

Abstract

We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically constrained path integral that includes a summation over \mathrm{U}\left(1\right) topological charge. We derive an effective quantum action for the BH model, which enables a non-perturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.