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

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.

12 pages, 11 figures

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• Nonlinear symmetry breaking of Aharonov-Bohm cages
• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Non-Abelian Aharonov-Bohm Caging in Photonic Lattices
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons
• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• Environmental Quantum States Trigger Emission in Nonlinear Photonics