Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux

TL;DR

This paper investigates the ground-state phase diagrams of a two-leg Bose-Hubbard ladder under magnetic flux, revealing population-imbalance instability and phase transitions, with special stabilization at flux $ ext{pi}$ due to umklapp processes.

Contribution

It provides a detailed analysis of phase transitions and population-imbalance instability in a Bose-Hubbard ladder with magnetic flux using multiple theoretical approaches.

Findings

Population-imbalance instability occurs for certain parameters.

A quantum phase transition similar to the ferromagnetic XXZ model is observed.

At flux  ext{pi}, a superfluid with chirality is stabilized, preventing phase transition.

Abstract

We consider a two-leg Bose-Hubbard ladder in the presence of a magnetic flux. We make use of Gross-Pitaevskii, Bogoliubov, bosonization, and renormalization group approaches to reveal a structure of ground-state phase diagrams in a weak-coupling regime relevant to cold atom experiments. It is found that except for a certain flux $\phi=\pi$, the system shows different properties as changing hoppings, which also leads to a quantum phase transition similar to the ferromagnetic XXZ model. This implies that population-imbalance instability occurs for certain parameter regimes. On the other hand, for $\phi=\pi$, it is shown that an umklapp process caused by commensurability of a magnetic flux stabilizes a superfluid with chirality and the system does not experience such a phase transition.