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arXiv:hep-th/9906205 · Nuclear Physics B

Bosonization at finite temperature and anyon condensation

Antonio Liguori, Mihail Mintchev, Luigi Pilo B

Published Mar 1, 2000• 43 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(99)00774-9

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Physical review. B, Condensed matter•Jan 1, 1993•7 citations
In this letter we study 1+1 anyon fields at finite temperature and density with non-vanishing chemical potentials. Our approach is based on an operator formalism for bosonization at finite temperature; the correlation functions for the system are given in an explicit form. Two are the main results of this construction: we point out the existence of persistent currents in 1+1 anyon systems; from the analysis of 2-point anyon field correlation function, a remarkable and new condensation phenomenon in momentum space is discovered. As a concrete example, the above formalism is applied to the Thirring model.
The large-distance asymptotic behavior of the field-field correlators has been computed for one-dimensional impenetrable anyons at finite temperatures. The asymptotic behavior agrees with the predictions of conformal field theory at low temperatures and reproduces the known results for impenetrable bosons and free fermions in appropriate limits. We have also obtained an integrable system of partial nonlinear differential equations which completely characterizes the 2-point correlation functions. The system is the same as for bosons but with different initial conditions.
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.