Topological BF theory of the quantum hydrodynamics of incompressible polar fluids

Apoorv Tiwari, Xiao Chen, Titus Neupert, Luiz H. Santos, Shinsei Ryu, Claudio Chamon, and Christopher Mudry
Phys. Rev. B 90, 235118 – Published 10 December 2014

Abstract

We analyze a hydrodynamical model of a polar fluid in (3 + 1)-dimensional spacetime. We explore a spacetime symmetry (volume-preserving diffeomorphisms) to construct an effective description of this fluid in terms of a topological BF theory. The two degrees of freedom of the BF theory are associated with the mass (charge) flows of the fluid and its polarization vorticities. We discuss the quantization of this hydrodynamic theory, which generically allows for fractionalized excitations. We propose an extension of the Girvin-MacDonald-Platzman algebra to (3 + 1)-dimensional spacetime by the inclusion of the vortex-density operator in addition to the usual charge density operator and show that the same algebra is obeyed by massive Dirac fermions that represent the bulk of Z2 topological insulators in three-dimensional space.

  • Figure
  • Received 2 September 2014
  • Revised 18 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.235118

©2014 American Physical Society

Authors & Affiliations

Apoorv Tiwari1, Xiao Chen1, Titus Neupert2, Luiz H. Santos3, Shinsei Ryu1, Claudio Chamon4, and Christopher Mudry5

  • 1Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
  • 2Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 4Physics Department, Boston University, Boston, Massachusetts 02215, USA
  • 5Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

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Issue

Vol. 90, Iss. 23 — 15 December 2014

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