Quantum critical scaling behavior of deconfined spinons

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to N=2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $\eta$ for the decay of the two-spin correlation function to first-order in $\epsilon=4-d$. We also note the scaling relation $\eta=d+2(1-\phi/\nu)$ connecting the exponent $\eta$ for the decay to the correlation length exponent $\nu$ and the crossover exponent $\phi$.Comment: 4.1 pages, no figures, references added; Version accepted for publication in PRB (RC

Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.Comment: 15 pages, 16 figure

Dislocation-Mediated Melting in Superfluid Vortex Lattices

We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -- rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.Comment: 9 pages, 2 figure

Preemptive vortex-loop proliferation in multicomponent interacting Bose--Einstein condensates

We use analytical arguments and large-scale Monte Carlo calculations to investigate the nature of the phase transitions between distinct complex superfluid phases in a two-component Bose--Einstein condensate when a non-dissipative drag between the two components is being varied. We focus on understanding the role of topological defects in various phase transitions and develop vortex-matter arguments allowing an analytical description of the phase diagram. We find the behavior of fluctuation induced vortex matter to be much more complex and substantially different from that of single-component superfluids. We propose and investigate numerically a novel drag-induced ``preemptive vortex loop proliferation'' transition. Such a transition may be a quite generic feature in many multicomponent systems where symmetry is restored by a gas of several kinds of competing vortex loops.Comment: 12 pages, 10 figures. Submitted to Physical Review

Effects of boundaries and density inhomogeneity on states of vortex matter in Bose--Einstein condensates at finite temperature

Most of the literature on quantum vortices predicting various states of vortex matter in three dimensions at finite temperatures in quantum fluids is based on an assumption of an extended and homogeneous system. It is well known not to be the case in actual Bose--Einstein condensates in traps which are finite systems with nonuniform density. This raises the question to what extent one can speak of different aggregate states of vortex matter (vortex lattices, liquids and tensionless vortex tangle) in these system. To address this point, in the present work we focus on the finite-size, boundaries and density inhomogeneity effects on thermal vortex matter in a Bose--Einstein condensate. To this end we perform Monte Carlo simulations on a model system describing trapped Bose--Einstein condensates. Throughout the paper, we draw on analogies with results for vortex matter obtained for extended systems. This work suggests that finiteness and intrinsic inhomogeneity of the system not withstanding, one nonetheless can approximately invoke the notion of distinct aggregate states of vortex matter realized at certain length scales. This might be helpful, in particular in search of possible new states of vortex matter in Bose--Einstein condensates with multiple components and different symmetries.Comment: 15 pages, 13 figures. Submitted to Physical Review A. High resolution pictures will be available in published versio

Effects of boundaries and density inhomogeneity on states of vortex matter in Bose-Einstein condensates at finite temperature

Most of the literature on quantum vortices predicting various states of vortex matter in three dimensions at finite temperatures in quantum fluids is based on the assumption of an extended and homogeneous system. This is well known not to be the case in actual Bose-Einstein condensates in traps, which are finite systems with nonuniform density. This raises the question to what extent one can speak of different aggregate states of vortex matter (vortex lattices, liquids, and tensionless vortex tangles) in these systems. To address this point, in the present work we focus on the finite-size, boundaries and density inhomogeneity effects on thermal vortex matter in a Bose-Einstein condensate. To this end we perform Monte Carlo simulations on a model system describing trapped Bose-Einstein condensates. Throughout the paper, we draw on analogies with results for vortex matter obtained for extended systems. We also consider, for comparison, the cylindrical confinement geometry with uniform density profile from the center out to the edge of the trap. The trapping potential is taken to be generically of an anharmonic form in such a way as to interpolate between a harmonic trap and a cylindrical confinement geometry. It also allows for a dip in the density profile at the center. We find distinct thermal equilibrium properties of the vortex system as the qualitative characteristics of the trapping potential are varied. For a uniform cylindrical confinement geometry, we find a vortex lattice at the center of the trap as well as ringlike thermal fluctuations of the vortex system as the trap edge is approached. For a harmonic trap, we find a distinct region at the edge of the trap where the vortex lines appear to have lost their line tension. Due to the steep density gradient, this crosses directly over to a vortex-line lattice at the center of the trap at low temperatures. At higher temperatures, an intermediate tensionful vortex liquid may exist. For an anharmonic trap where the ground state condensate density features a local minimum at the center of the trap, we find a corresponding region which appears to feature a tensionless vortex-line liquid phase. This work suggests that, finiteness and intrinsic inhomogeneity of the system notwithstanding, one nonetheless can approximately invoke the notion of distinct aggregate states of vortex matter realized at certain length scales. This might be helpful, in particular, in the search for possible new states of vortex matter in Bose-Einstein condensates with multiple components and different symmetries

Crossover States of Vortex Matter in Trapped Bose Condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He, the latter is relevant to a rotating trapped Bose condensate. In the former case we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tension-less vortex tangle near the edge of the trap. At higher temperatures an intermediate tension-full vortex liquid located between the vortex solid and the vortex tangle, may exist