We study a one-dimensional system of interacting anyons with short-range interactions under external confinement. This model, which describes anyons with zero-range
s-wave and
p-wave scattering interactions in the strong interaction regime, continuously interpolates between spin-polarized fermions with
p-wave interactions and free bosons. At zero temperature, the correlation functions decay exponentially with distance, with oscillations governed by the statistics parameter. The decay rate is maximal for
p-wave fermions and decreases monotonically as the statistics parameter approaches the bosonic limit, where it vanishes. The momentum distribution is asymmetric, a hallmark of one-dimensional anyons, and takes the form of a shifted Lorentzian with universal power-law tails, ${lim}_{k\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}}n(k)\ensuremath{\sim}C/{k}^{2}$. We prove analytically that, following release from a harmonic trap, the asymptotic momentum distribution converges to that of free bosons in the same trap, a phenomenon known as dynamical bosonization. We also establish the universality of the ground-state
n-particle reduced density matrices: their natural occupations are independent of the confining potential, while the associated natural
n-point functions for different confinements are related through a simple analytical transformation. In particular, for the one-particle reduced density matrix, we derive exact expressions for both the natural occupations and the natural orbitals at arbitrary particle number. These results extend and unify earlier partial findings for
p-wave fermions, and they provide a clear conceptual explanation of the double degeneracy observed in their spectrum.
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.
The main objective of this paper is to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real time formalism of Thermofield Dynamics. Formally the results parallel those of the T = 0 case. The well known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. In order to emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized.
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents that characterize spontaneous flows in the system. In this Letter, we consider quantum many-body systems on a finite one-dimensional lattice and discuss the scaling of the persistent currents as a function of the system size. We show that, when the conserved quantities are given as the Noether charges associated with internal symmetries or the Hamiltonian itself, the corresponding persistent currents can be bounded by a correlation function of two operators at a distance proportional to the system size, implying that they decay at least algebraically as the system size increases. In contrast, the persistent currents of accidentally conserved quantities can be nonzero even in the thermodynamic limit and even in the presence of the time-reversal symmetry. We discuss "the current of energy current" in S=1/2 XXZ spin chain as an example and obtain an analytic expression of the persistent current.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.
This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.