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Physical review. B, Condensed matter

Kosterlitz-Thouless-Berezinskii transition in the one-dimensional quantum roughening model

Rosario Fazio, G. Falci, Gaetano Giaquinta

Published Feb 1, 1992• 0 citations
Publisher

Abstract

We present numerical simulations of the one-dimensional quantum roughening model. We show that the system undergoes a zero-temperature phase transition of the Kosterlitz-Thouless-Berezinskii type. This transition leads to a superfluid state (nondissipative mass transfer). The mechanism responsible for this transition is very similar to that of the phase transition in two-dimensional smectic crystals.

DOI
10.1103/physrevb.45.2779

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We present numerical simulations of the one-dimensional quantum roughening model. We show that the system undergoes a zero-temperature phase transition of the Kosterlitz-Thouless-Berezinskii type. This transition leads to a superfluid state (nondissipative mass transfer). The mechanism responsible for this transition is very similar to that of the phase transition in two-dimensional smectic crystals.
We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕21∕21∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional U(1)\mathrm{U}(1)U(1) universality class and the interface remains smooth. Similar phenomena are expected for domain walls in quantum antiferromagnets.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models these are vortices: above a transition temperature TBKTT_{\rm BKT}TBKT​ vortices are free, below this transition temperature they get confined. In this work we extend the concept of BKT transition to quantum systems in two dimensions. In particular, we demonstrate that a zero-temperature quantum BKT phase transition, driven by a coupling constant can occur in 2D models governed by an effective gauge field theory with a diverging dielectric constant. One particular example is that of a compact U(1) gauge theory with a diverging dielectric constant, where the quantum BKT transition is induced by non-relativistic, purely 2D magnetic monopoles, which can be viewed also as electric vortices. These quantum BKT transitions have the same diverging exponent zzz as the quantum Griffiths transition but have nothing to do with disorder.
The Berezinskii–Kosterlitz–Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models, these are vortices: above a transition temperature TBKT, vortices are free; below this transition temperature, they get confined. In this work, we extend the concept of BKT transition to quantum systems in two dimensions. In particular, we demonstrate that a zero-temperature quantum BKT phase transition driven by a coupling constant can occur in 2D models governed by an effective gauge field theory with a diverging dielectric constant. One particular example is that of a compact U(1) gauge theory with a diverging dielectric constant, where the quantum BKT transition is induced by non-relativistic, purely 2D magnetic monopoles, which can be viewed also as electric vortices. These quantum BKT transitions have the same diverging exponent z as the quantum Griffiths transition but are not related to disorder.
We analyze the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the nonlinear Schr\"odinger model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first-order correlation function behave with respect to the mass, the energy, and the size of the system. By relating the free-particle energy to the temperature, we are able to estimate the Berezinskii-Kosterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size independent, leading to a power-law dependence of the condensate fraction with respect to the system size.
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to quantum one. As a result at small temperatures the critical exponent of the BKT transition, η=1/4η=1/4η=1/4, remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.
An easy-plane ferromagnetic spin-1 Bose gas undergoes two Berezinskii-Kosterlitz-Thouless transitions, associated with mass and spin superfluidity, respectively. We study the effect of axial magnetization on the superfluid properties of this system. We find that nonzero axial magnetization couples mass and spin superflow, via a mechanism analogous to the Andreev-Bashkin effect present in two-component superfluids. With sufficiently large axial magnetization mass and spin superfluidity arise simultaneously. The crossover to this phase provides a finite-temperature generalization of the zero-temperature broken-axisymmetric to easy-axis transition. We present analytic relations connecting mass and spin superfluidity with experimentally observable coherence of the three spinor components and local magnetization.