Vortex dynamics and Hall conductivity of hard-core bosons

2010/05/31 by Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas
Physics and Astronomy · #Boson #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Degenerate energy levels #Magnetic field #Magnetic flux #Magnetic flux quantum #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Semiclassical physics #Vortex #cond-mat.quant-gas #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.82.134510

published as Phys. Rev. B 82, 134510 (2010) · 15 pages, 15 figures

arxiv created 2010/06/09 · openalex publication_date 2010/10/07 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Magnetotransport of hard-core bosons is studied using an XXZ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex-hopping energy t_V, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at 6.5\ifmmode×\else\texttimes\fi10^\ensuremath-3 vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low-energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom, which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices and magnet transport of short coherence length superconductors.

Citations

• Putting competing orders in their place near the Mott transition. II. The doped quantum dimer model
• Analytical and numerical study of hardcore bosons in two dimensions
• Finite-temperature superfluid density in very underdoped cuprates
• Observability of Quantum Phase Fluctuations in Cuprate Superconductors
• Plaquette boson-fermion model of cuprates
• Dynamical vortices in superfluid films
• Vortex configurations of bosons in an optical lattice
• 4D-XY quantum criticality in a doped Mott insulator
• Fractional Quantum Hall States of Atoms in Optical Lattices
• Charge Modulation, Spin Response, and Dual Hofstadter Butterfly in High-TcCuprates
• The cold atom Hubbard toolbox
• Conductivity of hard core bosons: A paradigm of a bad metal
• Quantised singularities in the electromagnetic field,
• Putting competing orders in their place near the Mott transition
• Quantum Magnetism Approaches to Strongly Correlated Electrons