The exciton Bose liquid (EBL) is a hypothesized phase of bosons in 2+1D which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this note, we discuss an RG scheme that can be used to address the stability of this and related phases of matter. We argue that in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can likely be used to realize a stable phase, without the need for fine-tuning. A simple generalization to 3+1D is also discussed.
The exciton Bose liquid (EBL) is a hypothesized phase of bosons in
2+1D which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this paper, we discuss a renormalization group scheme that can be used to address the stability of this and related phases of matter. We find that, in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can be used to realize a stable phase, without the need for fine-tuning. A simple generalization to
3+1D is also discussed.
We present a quantum Monte Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a K1 term acts on 1×1 plaquettes and a K2 term acts on 1×2 and 2×1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small K2, valence bond solid for intermediate K2, and possibly for large K2 the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al [Phys. Rev. B 66, 054526 (2002)10.1103/PhysRevB.66.054526]. Away from half-filling, the EBL phase is present already for intermediate K2 and remains stable for a range of densities below 1/2 before phase separation sets in at lower densities.
Slave particle approaches are widely used in studies of exotic quantum phases. A complete description beyond mean field also contains dynamical gauge fields, while a simplified procedure considers Gutzwiller-projected trial states. We apply this in the context of bosonic models with ring exchanges realizing so-called exciton Bose liquid (EBL) phase and compare a Gutzwiller wave function against an accurate EBL wave function. We solve the parton-gauge theory and show that dynamical fluctuations of the spatial gauge fields are necessary for obtaining qualitatively accurate EBL description. On the contrary, just the Gutzwiller projection leads to a state with subtle differences in the long-wavelength properties, thus suggesting that Gutzwiller wave functions may generally fail to capture long-wavelength physics.
We investigate a hard-core boson model with ring-only exchanges on a square lattice, where a
K1 term acts on 1$\ifmmode\times\else\texttimes\fi{}$1 plaquettes and a
K2 term acts on 1$\ifmmode\times\else\texttimes\fi{}
2and2\ifmmode\times\else\texttimes\fi{}$1 plaquettes, with a goal of realizing a novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al. [Phys. Rev. B 66, 054526 (2002)]. We construct Jastrow-type variational wave functions for the EBL, study their formal properties, and then use them as seeds for a projective quantum Monte Carlo study. Using the Green's function Monte Carlo approach, we obtain an unbiased phase diagram that at half-filling reveals a charge density wave for small
K2, a valence bond solid for intermediate
K2, and possibly for large
K2 the EBL phase. Away from half-filling, the EBL phase is present for intermediate
K2 and remains stable for a range of densities below 1/2 before phase separation occurs at lower densities.
It is well-known that a stable algebraic spin liquid state (or equivalently an algebraic Bose liquid (ABL) state) with emergent gapless photon excitations can exist in quantum spin ice systems, or in a quantum dimer model on a bipartite
3d lattice. This photon phase is stable against any weak perturbation without assuming any symmetry. Further works concluded that certain lattice models give rise to more exotic stable algebraic Bose liquid phases with graviton-like excitations. In this paper we will show how these algebraic Bose liquid states can be generalized to stable phases with even more exotic types of gapless excitations and then argue that these new phases are stable against weak perturbations. We also explicitly show that these theories have an (algebraic) topological ground state degeneracy on a torus, and construct the corresponding topological invariants.
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.