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Physical review. B, Condensed matter

Long-range order of two interacting anyon-gas layers of opposite statistical charge

C. A. A. de Carvalho, D. Boyanovsky

Published Jan 1, 1993• 7 citations
Publisher

Abstract

We study aspects of long-range order in a model consisting of two interacting layers of anyon gases with opposite statistical charge. We start with bosons with a statistical interaction and second quantize the theory using an approach that uses a local and gauge-invariant order parameter. We then study this model in the Bogoliubov approximation. We explicitly compute the depletion from the condensate and gauge-invariant correlation functions. We show that the ground state is a ``weak'' condensate of charge-flux composites with ``nearly long-range order.'' The condensate becomes statistically neutral in the thermodynamic limit. It is pointed out that the ``nearly long-range order'' at zero temperature has its origins in the logarithmic infrared singularities arising from the two-dimensional Coulomb repulsion induced by the long-range statistical interaction. The quasiparticle spectrum consists of one massless mode, and a plasmon mode with a weak gap. The system is quasiordered at any nonzero temperature, but we present evidence for a finite helicity modulus.

DOI
10.1103/physrevb.47.334

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We study aspects of long-range order in a model consisting of two interacting layers of anyon gases with opposite statistical charge. We start with bosons with a statistical interaction and second quantize the theory using an approach that uses a local and gauge-invariant order parameter. We then study this model in the Bogoliubov approximation. We explicitly compute the depletion from the condensate and gauge-invariant correlation functions. We show that the ground state is a weak'' condensate of charge-flux composites with nearly long-range order.'' The condensate becomes statistically neutral in the thermodynamic limit. It is pointed out that the ``nearly long-range order'' at zero temperature has its origins in the logarithmic infrared singularities arising from the two-dimensional Coulomb repulsion induced by the long-range statistical interaction. The quasiparticle spectrum consists of one massless mode, and a plasmon mode with a weak gap. The system is quasiordered at any nonzero temperature, but we present evidence for a finite helicity modulus.
We review aspects of broken symmetry and the nature of long range order in theories of anyons starting with bosons with a statistical interaction. We introduce a novel gauge invariant quantization scheme that allows the identification of local and gauge invariant order parameters. The connection between spin and statistics is reviewed and the consequences of broken symmetries in the anyon representation are discussed. An anyon gas is studied in the Bogoliubov approximation, it is determined that the ground state is a condensate of charge-flux composites with “quasi-long-range order” at zero temperature, a “weak” gap in the spectrum and finite helicity modulus. The system is disordered at nonzero temperatures. The disorder is not caused by Goldstone bosons but by the strong infrared behavior arising from the Coulomb interaction induced by the long-range statistical interaction. The properties of topological vortices in nonrelativistic and in relativistic Landau-Ginzburg theories are studied in detail. We study the physics of the mean-field ansatz and quasi-long range order in a simple exactly soluble relativistic model. This model exhibits a novel phenomenon of charge redistribution to the boundaries and restoration of translational invariance in the infinite volume limit. It also illuminates the physics of quasi-long-range order with a gap in the spectrum, statistical charge polarization by external magnetic fields and the role of “large” gauge transformations.
We study the physics of the mean field ansatz in a simplified anyon model. The model is solved exactly in a finite geometry with particular attention to boundary conditions compatible with a mean statistical magnetic field. The spectrum consists of bosonic plasma-like density fluctuations with a gap. We find that the repulsive Coulomb interactions introduced by the fluctuations around the mean field force the statistical charge and magnetic field to become localized near the boundaries. Translational invariance, broken by the mean field, is restored in the infinite volume limit as the statistical charge and magnetic field escape to infinity. The polarization effects of an external magnetic field and the role of “large” gauge transformations are also studied.
Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields Hc1{\mathit{H}}_{\mathit{c}1}Hc1​\ensuremath{\ll}H\ensuremath{\ll}Hc2{\mathit{H}}_{\mathit{c}2}Hc2​, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.
The work of an earlier paper on the ground-state properties of a system of bosons interacting via a strong short-ranged repulsive potential and a weak long-ranged attractive potential is extended to nonzero temperatures. The technique of temperature-dependent Green's functions is employed. It is shown that with the same restrictions on the two-body potential as imposed in the case of the ground state, it is possible to calculate in a consistent fashion the leading low-temperature contributions to the various thermodynamic functions. The results provide support for Landau's point of view for treating the system at low temperatures as a collection of noninteracting quasiparticles. The isotherms of the system at the low temperatures considered indicate a first-order transition between a phase with a condensate and one without a condensate, and also the possibility, at higher temperatures, of three phases.
Using notions of supersymmetry, we present an exactly soluble model of anyons with both statistical and scalar interactions in 2+1 dimensions. We demonstrate that half-statistics particles with two spin flavors condense into a local singlet state which is both a charge superfluid and a ``spin metal'' in the sense that there is charge-pairing off-diagonal long-range order with gapless charge excitations, but a gap in the collective spin-mode spectrum. The present results shed considerable light on the mean-field theory of fractional statistics.
We construct and study relativistic anyons in 1+11+11+1 dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by adding density-density interactions, as in the Luttinger model, and (ii) by coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a nonzero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics.