Universal low-temperature properties of quantum and classical ferromagnetic chains

We identify the critical theory controlling the universal, low temperature, macroscopic properties of both quantum and classical ferromagnetic chains. The theory is the quantum mechanics of a single rotor. The mapping leads to an efficient method for computing scaling functions to high accuracy.Comment: 4 pages, 2 tables and 3 Postscript figure

Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice

We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.Comment: 10 pages, 9 figure

Mott insulators in strong electric fields

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

Three dimensional resonating valence bond liquids and their excitations

We show that there are two types of RVB liquid phases present in three-dimensional quantum dimer models, corresponding to the deconfining phases of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite cubic lattice and is the generalization of the critical point in the square lattice quantum dimer model found originally by Rokhsar and Kivelson. The latter exists on the non-bipartite face-centred cubic lattice and generalizes the RVB phase found earlier by us on the triangular lattice. We discuss the excitation spectrum and the nature of the ordering in both cases. Both phases exhibit gapped spinons. In the U(1) case we find a collective, linearly dispersing, transverse excitation, which is the photon of the low energy Maxwell Lagrangian and we identify the ordering as quantum order in Wen's sense. In the Z_2 case all collective excitations are gapped and, as in d=2, the low energy description of this topologically ordered state is the purely topological BF action. As a byproduct of this analysis, we unearth a further gapless excitation, the pi0n, in the square lattice quantum dimer model at its critical point.Comment: 9 pages, 2 figure

Behaviour of the energy gap near a commensurate-incommensurate transition in double layer quantum Hall systems at nu=1

The charged excitations in the system of the title are vortex-antivortex pairs in the spin-texture described in the theory by Yang et al which, in the commensurate phase, are bound together by a ``string''. It is shown that their excitation energy drops as the string lengthens as the parallel magnetic field approaches the critical value, then goes up again in the incommensurate phase. This produces a sharp downward cusp at the critical point. An alternative description based on the role of disorder in the tunnelling and which appears not to produce a minimum in the excitation energy is also discussed. It is suggested that a similar transition could also occur in compressible Fermi-liquid-like states.Comment: latex file, 17 page

Quantum field theory of metallic spin glasses

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains reference to related work in cond-mat/950412

Lattice gauge theory with baryons at strong coupling

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.Comment: 31 pages, 5 EPS figures. Corrected Eq. (6.1

Chern-Simons Theory for Magnetization Plateaus of Frustrated J1J_1-J2J_2 Heisenberg model

The magnetization curve of the two-dimensional spin-1/2 $J_1$-$J_2$ Heisenberg model is investigated by using the Chern-Simons theory under a uniform mean-field approximation. We find that the magnetization curve is monotonically increasing for $J_2/J_1 < 0.267949$, where the system under zero external field is in the antiferromagnetic N\'eel phase. For larger ratios of $J_2/J_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M/M_{\rm sat}=1/2$ plateau and predicts a new plateau at $M/M_{\rm sat}=1/3$. By identifying the onset ratio $J_2/J_1$ for the appearance of the 1/2-plateau with the boundary between the N\'eel and the spin-disordered phases in zero field, we can determine this phase boundary accurately by this mean-field calculation. Verification of these interesting results would indicate a strong connection between the frustrated antiferromagnetic system and the quantum Hall system.Comment: RevTeX 4, 4 pages, 3 EPS figure

Simultaneous Diagonal and Off Diagonal Order in the Bose--Hubbard Hamiltonian

The Bose-Hubbard model exhibits a rich phase diagram consisting both of insulating regimes where diagonal long range (solid) order dominates as well as conducting regimes where off diagonal long range order (superfluidity) is present. In this paper we describe the results of Quantum Monte Carlo calculations of the phase diagram, both for the hard and soft core cases, with a particular focus on the possibility of simultaneous superfluid and solid order. We also discuss the appearance of phase separation in the model. The simulations are compared with analytic calculations of the phase diagram and spin wave dispersion.Comment: 28 pages plus 24 figures, uuencoded Revtex+postscript file

The 6dF galaxy survey: fundamental plane data

We report the 6dFGS Fundamental Plane (6dFGSv) catalogue that is used to estimate distances and peculiar velocities for nearly 9000 early-type galaxies in the local (z < 0.055) universe. Velocity dispersions are derived by cross-correlation from 6dF V-band spectra with typical S/N of 12.9 Å−1 for a sample of 11 315 galaxies; the median velocity dispersion is 163 km s−1 and the median measurement error is 12.9 per cent. The photometric Fundamental Plane (FP) parameters (effective radii and surface brightnesses) are determined from the JHK 2MASS images for 11 102 galaxies. Comparison of the independent J- and K-band measurements implies that the average uncertainty in XFP, the combined photometric parameter that enters the FP, is 0.013 dex (3 per cent) for each band. Visual classification of morphologies was used to select a sample of nearly 9000 early-type galaxies that form 6dFGSv. This catalogue has been used to study the effects of stellar populations on galaxy scaling relations, to investigate the variation of the FP with environment and galaxy morphology, to explore trends in stellar populations through, along and across the FP, and to map and analyse the local peculiar velocity field