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We have studied how substitutions of magnetic Ni and nonmagnetic Zn in copper sites of Y3Ba5Cu8O18–δ (Y-358) affect critical temperature and the nonlinear behavior of current–voltage (IV) characteristics in the zero magnetic field. An exponent as a function of temperature (T) has been extracted to understand nonlinearity of IV within the framework of the BKT transition. We have extracted superfluid phase stiffness as a function of T of both groups of samples using the nonlinear exponent and the Ambegaokar–Halperin–Nelson–Siggia (AHNS) theory. The linear nature of the suppression of the critical temperature by Zn is found to be stronger than that of Ni. A strong suppression of the superfluid phase stiffness (SPS) by both dopants has also been observed. However, the suppression of the SPS with T by the nonmagnetic Zn is entirely different in comparison with the nonlinear suppression by the magnetic Ni. [ABSTRACT FROM AUTHOR]

We present an overview of selected copper-based quasi-2D square-lattice spin-1/2 materials with an easy-plane anisotropy, providing the possibility to study emergent Berezinskii-Kosterlitz-Thouless (BKT) correlations. In particular, in those materials with a comparatively small exchange coupling, the effective XY anisotropy of the low-temperature spin correlations can be controlled by an applied magnetic field, yielding a systematic evolution of the BKT correlations. In cases where the residual interlayer correlations are small enough, dynamical BKT correlations in the critical regime may be observed experimentally, whereas the completion of the genuine BKT transition is preempted by the onset of long-range order. [ABSTRACT FROM AUTHOR]

Superconducting nanofilms are tunable systems that can host a 3D–2D dimensional crossover leading to the Berezinskii–Kosterlitz–Thouless (BKT) superconducting transition approaching the 2D regime. Reducing the dimensionality further, from 2D to quasi-1D superconducting nanostructures with disorder, can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase-fluctuation phenomena of difficult experiments. We characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature-dependent resistivity and current–voltage (I-V) characteristics. Our measurements evidence clear features related to the emergence of BKT transition and PS events. The contemporary observation in the same system of BKT transition and PS events, and their tunable evolution in temperature and thickness was explained as due to the nano-conducting paths forming in a granular NbN system. In one of the investigated samples, we were able to trace and characterize the continuous evolution in temperature from quantum to thermal PS. Our analysis established that the detected complex phase phenomena are strongly related to the interplay between the typical size of the nano-conductive paths and the superconducting coherence length. [ABSTRACT FROM AUTHOR]

In this paper, we study the von Neumann entanglement entropy as a measure of the quantum entanglement in the spin-1 two-dimensional XX model with single-ion anisotropy. We use the bond operator formalism and consider the range of large anisotropy D and in the neighborhood of the critical point D c . One discusses the influence of the Berezinskii–Kosterlitz–Thouless phase transition (BKT) that occurs at critical anisotropy point D c , or the transition of the topological order of vortices and disordered phase on quantum entanglement. [ABSTRACT FROM AUTHOR]

In this paper, we use the Replica-Exchange Wang–Landau (REWL) technique to study the behavior of the two-point correlation function of the site diluted classical anisotropic Heisenberg (AH) model in two dimensions. The model has a topological Berezinskii–Kosterlitz–Thouless (BKT) transition for any dilution down to the percolation threshold, ρ th ≈ 0. 5 9 2 7 5. Contrary to earlier results that predict the exponent of the correlation function, η , to decay linearly to zero as a function of temperature, we found that it decreases with temperature to a finite value η 0 at T → 0 for any dilution ρ th ≤ ρ ≤ 1. [ABSTRACT FROM AUTHOR]

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J ) by the presence of a diagonal crossing (coupling constant J ′ ) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the O ( 3 ) symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an O ( 2 ) symmetry, a Berezinskii–Kosterlitz–Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants J ′ and D . The problem is developed through a continuous representation given by the O ( 3 ) Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model. [ABSTRACT FROM AUTHOR]

In this work we use the Self Consistent Harmonic Approximation and Quantum Monte Carlo technique to study the Quantum X Y on a two dimensional square lattice in the presence of nonmagnetic impurities. In particular we discuss how site disorder changes the Berezinskii–Kosterlitz–Thouless transition temperature, T B K T . This temperature is determined as a function of the nonmagnetic density. Our results are consistent with an anomalous behavior of T B K T at a concentration close to the site percolation threshold. We interpret the results as due to a competition between the confining of vortices and quantum fluctuations, or due to finite size effects. [ABSTRACT FROM AUTHOR]

Abstract: We derive a mean-field description for two-dimensional (2D) interacting Bose gases at arbitrary temperatures. We find that genuine Bose–Einstein condensation with long-range coherence only survives at zero temperature. At finite temperatures, many-body pairing effects included in our mean-field theory introduce a finite amplitude for the pairing density, which results in a finite superfluid density. We incorporate Berezinskii–Kosterlitz–Thouless (BKT) physics into our model by considering the phase fluctuations of our pairing field. This then leads to the result that the superfluid phase is only stable below the BKT temperature due to these phase fluctuations. In the weakly interacting regime at low temperature we compare our theory to previous results from perturbative calculations, renormalization group calculations as well as Monte Carlo simulations. We present a finite-temperature phase diagram of 2D Bose gases. One signature of the finite amplitude of the pairing density field is a two-peak structure in the single-particle spectral function, resembling that of the pseudogap phase in 2D attractive Fermi gases. [Copyright &y& Elsevier]

The phase behaviour of the Lebwohl-Lasher lattice gas model (one of the simplest representations of a nematogenic fluid) confined in a slab is investigated by means of extensive Monte Carlo simulations. The model is known to yield a first order gas-liquid transition in both the 2D and 3D limits, that is coupled with an orientational order-disorder transition. This latter transition happens to be first order in the 3D limit and it shares some characteristic features with the continuous defect mediated Berezinskii-Kosterlitz-Thouless transition in 2D. In this work we will analyze in detail the behaviour of this system taking full advantage of the lattice nature of the model and the particular symmetry of the interaction potential, which allows for the use of efficient cluster algorithms. [ABSTRACT FROM AUTHOR]

Abstract: A new “bond-algebraic” approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and p-clock models. By combining duality and Peierls arguments, we establish the existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when . This latter symmetry is associated with the appearance of discrete vortices and Berezinskii–Kosterlitz–Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for , is critical (massless) with decaying power-law correlations. [Copyright &y& Elsevier]

We study cold fermions in 2D that are interacting through the s-wave contact potential, using the path-integral formalism. The phase transitions are investigated using the joint solution of the gap and number equations. In the latter ones, the amplitude and phase fluctuations are taken into account within the t-matrix NSR-type formalism. It is shown that convergent solutions for the fermion density in 2D can be obtained even in the lowest-order (quadratic) approximation for fluctuations with a proper determination of the spectral functions. This approach leads, in particular, to a non-coherent quasicondensate which exists between the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature below which the system is superfluid and a transition temperature T above which the quasicondensate is destroyed. [ABSTRACT FROM AUTHOR]

Abstract: The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations. [ABSTRACT FROM AUTHOR]

Abstract: We use Monte Carlo to investigate the Berezinskii–Kosterlitz–Thouless transition close to the site percolation threshold in a square lattice. Several thermodynamic quantities are calculated for lattice sizes , from . Our results are consistent with an infinite order transition for any value of the concentration of magnetic sites. We found that close to the critical percolation concentration, (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as and the specific heat behaves as . [Copyright &y& Elsevier]

• The BKT transition on the spherical surface is studied. • A self-consistent formalism is used to determine the spin stiffness. • The role of the z-axis anisotropy is taken into account. • Quantum and semiclassical approaches are analyzed. The Berezinskii-Kosterlitz-Thouless (BKT) transition is a well-known phenomenon on planar surfaces; however, for curved spaces, the situation is not clear. In this work, we applied the Self-consistent Harmonic Approximation (SCHA) to study the XXZ ferromagnetic model on the spherical surface. The Hamiltonian is written in terms of the canonically conjugate fields (operators in the quantum formalism) S z and Φ that provide a renormalized spin stiffness depending on temperature. We consider both semiclassical and quantum approaches to the problem. The BKT transition is then determined by the temperature that provides abrupt vanishing of the spin stiffness. Our results show T BKT values close to that obtained for the planar model, and they are in agreement with the general aspects of the BKT phase transition theory. [ABSTRACT FROM AUTHOR]

We study vortex patterns of counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two “flavors” because there are two opposite directions of beam propagation. In a certain parameter range, the vortices form stable equilibrium configurations which we study using the methods of statistical field theory and generalize the Berezinsky-Kosterlitz-Thouless transition of the XY model to the “two-flavor” case. In the nonequilibrium regime, the patterns exhibit an Andronov-Hopf bifurcation which may lead to oscillations (limit cycle), chaos or decay to zero intensity due to radiation losses. We show how to identify various pathways toward instability from intensity patterns, i.e. from experiment. [ABSTRACT FROM AUTHOR]