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.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.

arXiv:cond-mat/0703261Physical Review BJun 21, 2007103 citations

Gauge-invariant response functions in algebraic Fermi liquids

Marcel Franz, T. Pereg-Barnea, Daniel E. Sheehy +1 more

A method is developed that permits a simple evaluation of two-loop response functions for fermions coupled to a gauge field. We employ this method to study the gauge-invariant response functions in the algebraic Fermi liquid, a non-Fermi liquid state proposed to describe the pseudogap phase in the ${\mathrm{QED}}_{3}$ theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.A method is developed that permits a simple evaluation of two-loop response functions for fermions coupled to a gauge field. We employ this method to study the gauge-invariant response functions in the algebraic Fermi liquid, a non-Fermi liquid state proposed to describe the pseudogap phase in the ${\mathrm{QED}}_{3}$ theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.

arXiv:cond-mat/0211119Physical review. B, Condensed matterJul 18, 200338 citations

Field correlation functions in a one-dimensional Bose gas

Anatoli G. Izergin, V. E. Korepin, Nicolai Reshetikhin

Journal of Mathematical SciencesJul 1, 19892 citations

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.

{\mathrm{QED}}_{3}

theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.