Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

We study a topological phase of interacting bosons in (3+1) dimensions which is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model which realizes this phase and which can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator. We also study the boundary between the topological insulator and a trivial insulator. We find a surface phase diagram which includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system. We also present models that realize symmetry-enriched topologically-ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.Comment: 26 pages, 16 figure

Nonmagnetic impurities in a S=(1/2) frustrated triangular antiferromagnet: Broadening of 13C NMR lines in κ-(ET)2Cu2(CN)3

We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of 13C NMR lines in the organic spin liquid material κ-(ET)2Cu2(CN)3. For high temperatures down to J/3, we calculate local susceptibility near a nonmagnetic impurity and near a grain boundary for the nearest-neighbor Heisenberg model in high-temperature series expansion. We find that the local susceptibility decays to the uniform one in few lattice spacings, and for a low density of impurities we would not be able to explain the line broadening present in the experiments already at elevated temperatures. At low temperatures, we assume a gapless spin liquid with a Fermi surface of spinons. We calculate the local susceptibility in the mean field and also go beyond the mean field by Gutzwiller projection. The zero-temperature local susceptibility decays as a power law and oscillates at 2kF. As in the high-temperature analysis we find that a low density of impurities is not able to explain the observed broadening of the lines. We are thus led to conclude that there is more disorder in the system. We find that a large density of pointlike disorder gives broadening that is consistent with the experiment down to about 5 K, but that below this temperature additional mechanism is likely needed

Origin of artificial electrodynamics in three-dimensional bosonic models

Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless "photon" excitation. In this paper we show how to view the physics of this "Coulomb" state in terms of the excitations of proximate superfluid. We argue for the presence of ordered vortex cores with a broken discrete symmetry in the nearby superfluid phase and that proliferating these degenerate but distinct vortices with equal amplitudes produces the Coulomb phase. This provides a simple physical description of the origin of the exotic excitations of the Coulomb state. The physical picture is formalized by means of a dual description of three-dimensional bosonic systems in terms of fluctuating quantum mechanical vortex loops. Such a dual formulation is extensively developed. It is shown how the Coulomb phase (as well as various other familiar phases) of three-dimensional bosonic systems may be described in this vortex loop theory. For bosons at half-filling and the closely related system of spin-1/2 quantum magnets on a cubic lattice, fractionalized phases as well as bond- or "box"-ordered states are possible. The latter are analyzed by an extension of techniques previously developed in two spatial dimensions. The relation between these "confining" phases with broken translational symmetry and the fractionalized Coulomb phase is exposed

Variational study of J_(1)-J_(2) Heisenberg model on kagome lattice using projected Schwinger-boson wave functions

Motivated by the unabating interest in the spin-1/2 Heisenberg antiferromagnetic model on the kagome lattice, we investigate the energetics of projected Schwinger-boson (SB) wave functions in the J_(1)-J_(2) model with antiferromagnetic J_(2) coupling. Our variational Monte Carlo results show that Sachdev’s Q_(1)=Q_(2) SB ansatz has a lower energy than the Dirac spin liquid for J_(2) ≳ 0.08J_(1) and the q=0 Jastrow-type magnetically ordered state. This work demonstrates that the projected SB wave functions can be tested on the same footing as their fermionic counterparts

Possible realization of the Exciton Bose Liquid phase in a hard-core boson model with ring-only exchange interactions

We investigate a hard-core boson model with ring-only exchanges on a square lattice, where a $K_1$ term acts on 1$\times$1 plaquettes and a $K_2$ term acts on 1$\times$2 and 2$\times$1 plaquettes, with a goal of realizing a novel Exciton Bose Liquid (EBL) phase first proposed by Paramekanti, et al [Phys. Rev. B {\bf 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 Green's Function Monte Carlo, we obtain an unbiased phase diagram which at half-filling reveals CDW for small $K_2$, valence bond solid for intermediate $K_2$, and possibly for large $K_2$ the EBL phase. Away from half-filling, the EBL phase is present for intermediate $K_2$ and remains stable for a range of densities below 1/2 before phase separation occurs at lower densities.Comment: 18 pages, 15 figure

Study of a hard-core boson model with ring-only interactions

We present a Quantum Monte Carlo study of a hardcore boson model with ring-only exchanges on a square lattice, where a $K_1$ term acts on 1$\times$1 plaquettes and a $K_2$ term acts on 1$\times$2 and 2$\times$1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small $K_2$, valence bond solid for intermediate $K_2$, and possibly for large $K_2$ the novel Exciton Bose Liquid (EBL) phase first proposed by Paramekanti, et al[Phys. Rev. B {\bf 66}, 054526 (2002)]. Away from half-filling, the EBL phase is present already for intermediate $K_2$ and remains stable for a range of densities below 1/2 before phase separation sets in at lower densitiesComment: 4 page

Failure of Gutzwiller-type wave function to capture gauge fluctuations: Case study in the exciton Bose liquid context

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

Possible Exciton Bose Liquid in a Hard-Core Boson Ring Model

We present a quantum Monte Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a K_1 term acts on 1×1 plaquettes and a K_2 term acts on 1×2 and 2×1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small K_2, valence bond solid for intermediate K_2, and possibly for large K_2 the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al [Phys. Rev. B 66, 054526 (2002)]. Away from half-filling, the EBL phase is present already for intermediate K_2 and remains stable for a range of densities below 1/2 before phase separation sets in at lower densities