Duality, Magnetic space group and their applications to quantum phases and phase transitions on bipartite lattices in several experimental systems

Abstract

By using a dual vortex method, we study phases such as superfluid, solids, supersolids and quantum phase transitions in a unified scheme in extended boson Hubbard models at and slightly away from half filling on bipartite optical lattices such as honeycomb and square lattice. We also map out its global phase diagram at $T=0$ of chemical potential versus the ratio of kinetic energy over the interaction. We stress the importance of the self-consistence condition on the saddle point structure of the dual gauge fields in the translational symmetry breaking insulating sides, especially in the charge density wave side. We find that in the translational symmetry breaking side, different kinds of supersolids are generic possible states slightly away from half filling. We propose a new kind of supersolid: valence bond supersolid (VB-SS). In this VB-SS, the density fluctuation at any site is very large indicating its superfluid nature, but the boson kinetic energies on bonds between two sites are given and break the lattice translational symmetries indicating its valence bound nature. Implications on possible future QMC simulations in both bipartite lattices are given. All these phases and phase transitions can be potentially realized in ultra-cold atoms loaded on optical bipartite lattices.

15 pages, 5 figures, REVTEX4, long version of arXiv:cond-mat/0503113 which will not be published

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• Theory of Bose-Einstein condensation in trapped gases
• "Deconfined" quantum critical points
• Quantum phases of dipolar bosons in optical lattices
• Quantum Magnetic Excitations from Stripes in Copper-Oxide Superconductors
• Optical Production of Ultracold Polar Molecules
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• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Quantum critical transport, duality, and M-theory
• A quantum fluid of metallic hydrogen suggested by first-principles calculations
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• The Ground State of the Pseudogap in Cuprate Superconductors
• Phase separation in supersolids
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• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Nature of the quantum phase transitions in the two-dimensional hardcore boson model
• Supersolids in the Bose-Hubbard Hamiltonian
• Putting competing orders in their place near the Mott transition
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• The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice
• Random magnetic field and quasi-particle transports in the mixed state of high T_{c} cuprates
• Ginsburg-Landau theory of supersolid
• Thermally generated vortices, gauge invariance and electron spectral function in the pseudo-gap regime
• Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems
• Abelian bosonization approach to quantum impurity problems
• The mobility of dual vortices in honeycomb, square, triangular, Kagome and dice lattices
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Cited by in corpus (13)

• Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential
• Light scattering detection of quantum phases of ultracold atoms in optical lattices
• Optical Bragg, atom Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices
• Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields
• Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra
• Classification of magnons in Rotated Ferromagnetic Heisenberg model and their competing responses in transverse fields
• Quantum phases, Supersolids and quantum phase transitions of interacting bosons in frustrated lattices
• Characterizing symmetry breaking patterns in a lattice by dual vortex degree of freedoms
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Quantum incommensurate Skyrmion crystals and Commensurate to In-commensurate transitions in cold atoms and materials with spin orbit couplings in a Zeeman field
• Response of a strongly interacting spin-orbit coupling system to a Zeeman field