d-wave correlated critical Bose liquids in two dimensions

Abstract

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.

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