Quantum phase transitions of interacting bosons on hyperbolic lattices

Abstract

The effect of many-body interaction in curved space is studied based on the extended Bose--Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction as $q$ in the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.

7 pages, 5 figures

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• Hyperbolic Topological Band Insulators
• Universality of Hofstadter butterflies on hyperbolic lattices
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• Non-Abelian hyperbolic band theory from supercells
• Selberg trace formula in hyperbolic band theory
• Symmetry and topology of hyperbolic Haldane models
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Hyperbolic non-Abelian semimetal
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Topological linear response of hyperbolic Chern insulators
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• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Hyperbolic Spin Liquids
• Superfluid-Mott insulator quantum phase transition in a cavity optomagnonic system
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Higher-dimensional Euclidean and non-Euclidean structures in planar circuit quantum electrodynamics
• Bose-Einstein condensation on hyperbolic spaces
• Bose-Einstein condensation in exotic lattice geometries
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Flat bands and band touching from real-space topology in hyperbolic lattices