Quantum rotor description of the Mott-insulator transition in the Bose-Hubbard model

Abstract

We present the novel approach to the Bose-Hubbard model using the $\mathrm{U}(1)$ quantum rotor description. The effective action formalism allows us to formulate a problem in the phase only action and obtain an analytical formulas for the critical lines. We show that the nontrivial $\mathrm{U}(1)$ phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges - winding numbers. The comparison presented results to recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.

arXiv commentaccepted to PRB

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• Frustration effects in rapidly rotating square and triangular optical lattices
• Reference data for phase diagrams of triangular and hexagonal bosonic lattices
• Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges
• Synthetic magnetic field effects on neutral bosonic condensates in quasi three-dimensional anisotropic layered structures
• Particle-hole character of the Higgs and Goldstone modes in strongly-interacting lattice bosons
• Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model
• First-order superfluid-Mott-insulator transition for quantum optical switching in cavity QED arrays with two cavity modes
• Quantum Rotors on the AB${}_2$ Chain with Competing Interactions
• Temperature-dependent excitation spectra of ultra-cold bosons in optical lattices
• Quantum critical properties of Bose-Hubbard models
• Finite Temperature Phase Diagram in Rotating Bosonic Optical Lattice
• Superfluid to Mott-insulator transition in an anizotropic two--dimensional optical lattice
• Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model
• A Quantum Theory of Cold Bosonic Atoms in Optical Lattices
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Finite temperature superfluid transition of strongly-correlated lattice bosons in various geometries
• Sign reversal of the boson-boson interaction potential in planar Bose-Fermi mixtures under a synthetic magnetic field
• Finite-temperature quantum rotor approach for ultracold bosons in optical lattices