Characterizing symmetry breaking patterns in a lattice by dual vortex degree of freedoms

Abstract

A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degree of freedoms on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states in the direct lattices. In addition to a checkerboard charge density wave (X-CDW) and a stripe CDW, we find a novel CDW-VBS phase which has both local CDW and local valence bond solid (VBS) orders. Implications on QMC simulations are addressed. The possible experimental realizations of cold atoms loaded on optical lattices are discussed.

4+ pages, 3 figures, REVTEX4-1, published in Philosophical Magazine, June 28, 2012

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• A High Phase-Space-Density Gas of Polar Molecules
• Quantum critical transport, duality, and M-theory
• Quantum Phases of Cold Polar Molecules in 2D Optical Lattices
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Supersolid phase with cold polar molecules on a triangular lattice
• Putting competing orders in their place near the Mott transition
• Three-body Interactions in one Dimension
• A striped supersolid phase and the search for deconfined quantum criticality in hard-core bosons on the triangular lattice
• Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings
• Light scattering detection of quantum phases of ultracold atoms in optical lattices
• The mobility of dual vortices in honeycomb, square, triangular, Kagome and dice lattices
• Duality, Magnetic space group and their applications to quantum phases and phase transitions on bipartite lattices in several experimental systems

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• 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 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
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Slow-Goldstone mode generated by order from quantum disorder and its experimental detection