The mobility of dual vortices in honeycomb, square, triangular, Kagome and dice lattices

Abstract

It was known that by a duality transformation, interaction bosons at filling factor $f=p/q$ hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating{\em dual} " magnetic field" whose average strength through a dual plaquette is equal to the boson density $f=p/q$.So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of $f=p/q$ flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux $f=p/q$ per plaquette on 5 most common bi-partisian and frustrated lattices such as square, honeycomb, triangular, dice and Kagome lattices. We also determine the number of minima and their locations in the lowest band. We numerically calculate the bandwidths of the lowest Hofstadter bands in these lattices and find that except the Kagome lattice at odd $q$, they all satisfy the exponential decay law $W=A{e}^{-cq}$ even at the smallest $q$. We determine $(A,c)$ for the 5 different lattices. When $q=2$, we find that the lowest Hofstadter band is completely flat for both Kagome and dice lattices. This indicates that the boson ground state at half filling with nearest neighbor hopping on Kagome and dice lattice is always a superfluid state,in contrast to the triangular lattice where the boson ground state was shown previously to undergo a transition from superfluid to supersolid state.

arXiv comment20 pages,15 figures,2 tables

References in corpus (8)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Supersolids in the Bose-Hubbard Hamiltonian
• Putting competing orders in their place near the Mott transition
• Superfluids and Supersolids on Frustrated 2D Lattices
• Superfluid-Insulator Transitions on the Triangular Lattice
• Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum
• Coulomb interaction at Superconductor to Mott-insulator transition

Cited by in corpus (18)

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• Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model
• Light scattering detection of quantum phases of ultracold atoms in optical lattices
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Duality, Magnetic space group and their applications to quantum phases and phase transitions on bipartite lattices in several experimental systems
• Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields
• Optical Bragg, atom Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model
• Classification of magnons in Rotated Ferromagnetic Heisenberg model and their competing responses in transverse fields
• Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra
• Characterizing symmetry breaking patterns in a lattice by dual vortex degree of freedoms
• 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
• Mott phases and quantum phase transitions of extended Bose-Hubbard models in 2+1 dimensions