d-wave correlated critical Bose liquids in two dimensions
We develop a description of a quantum liquid phase of interacting bosons confined in two dimensions that possesses relative d-wave two-body correlations. We refer to this stable quantum phase as a d-wave Bose liquid (DBL). The DBL has no broken symmetries, supports gapless boson excitations that reside on "Bose surfaces" in momentum space, and exhibits power-law correlation functions characterized by a manifold of continuously variable exponents. While the DBL can be constructed for bosons moving in the two-dimensional continuum, the state only respects the point group symmetries of the square lattice. On the square lattice, the DBL respects all symmetries and does not require a particular lattice filling. However, lattice effects do allow for the possibility of a second distinct phase, a quasilocal variant we refer to as a d-wave local Bose liquid (DLBL). Remarkably, the DLBL has short-range boson correlations and hence no Bose surfaces, despite sharing gapless excitations and other critical signatures with the DBL. Moreover, both phases are metals with a resistance that vanishes as a power of the temperature. We establish these results by constructing a class of many-particle wave functions for the DBL, which are time reversal invariant analogs of Laughlin's quantum Hall wave function for bosons in a half-filled Landau level. A gauge theory formulation leads to a simple mean field theory, and a suitable N-flavor generalization enables incorporation of gauge field fluctuations to deduce the properties of the DBL/DLBL in a controlled and systematic fashion. Various equal-time correlation functions thereby obtained are in qualitative accord with the properties inferred from the variational wave functions. We also identify a promising microscopic Hamiltonian that might manifest the DBL or DLBL, and perform a variational energetics study comparing other competing phases, including the superfluid. We suggest how the d-wave Bose liquid wave function can be suitably generalized to describe an itinerant non-Fermi-liquid phase of electrons on the square lattice with a no-double-occupancy constraint, a d-wave metal phase.
Additional Information© 2007 The American Physical Society (Received 21 March 2007; published 21 June 2007) We would like to acknowledge discussions with T. Senthil and A. Vishwanath, and thank Jason Alicea for help with some calculations. The work at KITP was supported by the National Science Foundation through Grants No. PHY-9907949 and No. DMR-0529399.
Published - MOTprb07.pdf