The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions

TL;DR

This paper investigates a one-dimensional Bose-Hubbard model with geometric frustration, revealing a novel pair-superfluid phase and analyzing its properties, phase diagram, and entanglement characteristics under magnetic flux influence.

Contribution

It introduces the pair-Luttinger liquid phase in a frustrated Bose-Hubbard chain and analyzes its properties and stability, expanding understanding of quantum phases in such systems.

Findings

Identification of a pair-superfluid phase due to frustration

Complete phase diagram including Mott-insulator, superfluid, and pair-superfluid phases

Distinct entanglement spectrum features for different superfluid phases

Abstract

We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid phase is very sensitive to changes away from perfect frustration (half-flux). We provide some proposals to make the model more resilient to variants away from perfect frustration. We also study the bipartite entanglement properties of the chain. We discover that, while the scaling of the block entropy pair-superfluid and of the single-particle superfluid leads to the same central charge, the properties of the low-lying entanglement spectrum levels reveal their fundamental difference.