Kosterlitz-Thouless Phase Transition Research Articles

Order- N cluster Monte Carlo method for spin systems with long-range interactions

An efficient O ( N ) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen–Wang algorithm, which requires O ( N 2 ) operations per Monte Carlo sweep if applied to long-range interacting models. In addition, it is shown that the total energy and the specific heat can also be measured in O ( N ) time. We demonstrate the efficiency of our algorithm over the conventional method and the O ( N log N ) algorithm by Luijten and Blöte. We also apply our algorithm to the classical and quantum Ising chains with inverse-square ferromagnetic interactions, and confirm in a high accuracy that a Kosterlitz–Thouless phase transition, associated with a universal jump in the magnetization, occurs in both cases.

Instability of dipole magnetoexcitons in quantum wells' and graphene superlattices

We propose the Bose–Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. For this system the instability of the ground state of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is found. The density of superfluid component n s ( T ) and the temperature of the Kosterlitz–Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.

Collective properties of magnetobiexcitons in quantum wells and graphene superlattices

The Bose-Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field are considered. The two different Hamiltonians of a dilute gas of magnetoexcitons with a dipole-dipole repulsion in superlattices, consisting of both QWs and graphene layers (GLs) in the limit of high magnetic field, have been reduced to one effective Hamiltonian---a dilute gas of two-dimensional excitons with the renormalized effective mass of the magnetoexciton, which depends on the magnetic field. This Hamiltonian does not include the vector potential. Moreover, for $N$ excitons we have reduced the problem of $2N\ifmmode\times\else\texttimes\fi{}2$-dimensional space onto the problem of $N\ifmmode\times\else\texttimes\fi{}2$-dimensional space by integrating over the coordinates of the relative motion of an electron and a hole. The instability of the ground state of the system of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is found. The stable system of indirect quasi-two-dimensional magnetobiexcitons, consisting of a pair of indirect excitons with opposite dipole moments, is considered. The density of the superfluid component ${n}_{s}(T)$ and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both the QW and graphene realizations.

Exotic magnetic structures in ultrathin helimagnetic holmium films

The problem of spin arrangement in ultrathin films of materials with competing medium-range interactions has been investigated by classical Monte Carlo simulations, assuming the model pertinent to bulk holmium. We find that in addition to distorted helical configurations at low temperature, unusual blocked phases---with some inner disordered planes intercalating ordered blocks and with the inner planes undergoing a Kosterlitz-Thouless phase transition as the temperature rises---may appear at intermediate temperature. The blocked phases turn out to be much more structured than those predicted by mean-field calculations, and their contribution to the static structure factor appear substantially indistinguishable from that corresponding to helical order thus constituting a challenge for their experimental probing by conventional elastic scattering techniques.

Bose-Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene

We propose experiments to observe Bose-Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetoexcitons in two-layer graphene. The energy spectrum of collective excitations, the sound spectrum, and the effective magnetic mass of magnetoexcitons are presented in the strong magnetic field regime. The superfluid density ${n}_{S}$ and the temperature of the Kosterlitz-Thouless phase transition ${T}_{c}$ are shown to be increasing functions of the excitonic density $n$ but decreasing functions of $B$ and the interlayer separation $D$.

Absence of vortex condensation in a two dimensional fermionicXYmodel

Motivated by a puzzle in the study of two-dimensional lattice quantum electrodynamics with staggered fermions, we construct a two-dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well-known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a noncompact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a Kosterlitz-Thouless transition.

On the type of a phase transition in the system of exciton polaritons in an optical microcavity

The type of a phase transition in the quasi-equilibrium system of exciton polaritons in a two-dimensional optical microcavity has been analyzed. It has been shown that, although the system contains two types of bosons undergoing mutual transformations into each other, only one phase transition to the superfluid state with the quasilong-range order occurs in the two-dimensional system. This phase transition is a Kosterlitz-Thouless phase transition. A new physical implementation—excitons in a photon crystal—has been proposed for the Bose condensation of exciton polaritons. The superfluid properties of the ordered phase are discussed, and the superfluid density and Kosterlitz-Thouless transition temperature have been calculated in the low-density approximation.

Non-equilibrium critical dynamics of the two-dimensional XY model with Hamiltonian equations of motion

Non-equilibrium critical dynamics of the two-dimensional XY model is investigated with Hamiltonian equations of motion. Critical relaxation starting from both ordered and random states is carefully analyzed, and the short-time dynamic scaling behavior is revealed. Logarithmic corrections to scaling are detected for relaxation with a random initial state, while power-law corrections to scaling are observed for relaxation with an ordered initial state. The static exponent η and dynamic exponent z are determined around and below the Kosterlitz–Thouless phase transition temperature. Our results show that the deterministic dynamics described by Hamiltonian equations is in the same universality class as the stochastic dynamics described by Monte Carlo algorithms and Langevin equations.

Spectral Sensitivity and Spectral Resolution of Superconducting Single-Photon Detectors

Single photon detectors based on meanders from 5-nm thin B1 niobium nitride nanostrips show moderate spectral resolution along with the spectral cut-off of the quantum efficiency occurring in the near-infrared spectral range. Beyond the cut-off there is a gradual decrease of the quantum efficiency. To describe the response beyond the cut-off we combine the previously developed hot-spot detection mechanism with the photon-induced unbinding of the vortex-antivortex pairs, which appear in the superconducting film below the Kosterlitz-Thouless phase transition. The detector responds to the absorption of a single photon with a voltage pulse whose amplitude depends on the photon energy. We report the observation of a photon-energy dependent statistical distribution of the pulse amplitude that defines the energy resolution of the detector. We analyzed the detector response to continuous and femtosecond-pulse radiation using broadband microwave amplifiers and a fast single-shot oscilloscope as well as integrating SQUID amplifiers. Our analysis suggests that both the amplitude and the duration of the response pulses are jointly controlled via the kinetic inductance of the meander line and the Joule power dissipated in the meander by the bias current.

Bose Glass and Superfluid Phases of Cavity Polaritons

We report the calculation of cavity exciton-polariton phase diagram including realistic structural disorder. With increasing density polaritons first undergo a quasiphase transition toward a Bose glass: the condensate is localized in at least one minimum of the disorder potential. A further increase of the density leads to a percolation process of the polariton fluid giving rise to a Kosterlitz-Thouless phase transition toward superfluidity. The spatial representation of the condensate wave function as well as the spectrum of elementary excitations are obtained from the Gross-Pitaevskii equation for all the phases.

Modified Kosterlitz-Thouless transition model for the temperature dependence of the resistivity of anisotropic superconductors

Based on the Kosterlitz-Thouless (KT) phase transition model of two-dimensional systems, by introducing the thermal activation energy and the mean height of the pinning landscape into the correlation length, a modified KT transition model has been proposed to study the temperature dependence of the resistivity transition in anisotropic superconductors. This modified KT transition model is consistent with the Coulomb-Gas (CG) scaling law and the Halperin-Nelson relation. And it is applied to study the scaling behavior of the resistivity transition of Tl2Ba2CaCu2Ox (Tl-2212) thin film under various intensities of magnetic field. The calculated mean height of the pinning landscape from the resistivity curve depends on the temperature linearly, which supports the proposed model.

Ground-state properties of a large Coulomb-blockaded quantum dot

Using renormalization-group techniques we analyze equilibrium properties of a large gated quantum dot coupled via a long and narrow channel to a reservoir of electrons. Treating the electrons in the channel as one-dimensional and interacting, we demonstrate that for nearly-open dot and not very strong spin fluctuations the ground-state properties as a function of the gate voltage are non-analytic at the points of half-integer average dot population. Specifically, the exact result of K. A. Matveev, Phys. Rev. B 51, 1743 (1995), that the dot capacitance shows periodic logarithmic singularities is rederived as a special case corresponding to non-interacting electrons. We demonstrate that this conclusion also holds in the presence of SU(2) spin symmetry, and argue that logarithmic singularities persist as long as the Coulomb blockade is destroyed which will be the case for sufficiently large tunneling and not very strong interparticle repulsions. We show that interparticle repulsions aid the Coulomb blockade to survive disordering effect of zero-point motion provided the tunneling is sufficiently weak. Upon increase of tunneling, the Coulomb blockade disappears through a Kosterlitz-Thouless phase transition characterized by a dot population jump whose magnitude is only determined by interparticle repulsions in the channel. Similar conclusions are applicable to systems without SU(2) spin symmetry except that the logarithmic singularity of the capacitance is replaced by a power-law non-analyticity whose exponent characterizes the degree of spin fluctuations.

Classical dimers with aligning interactions on the square lattice

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and transfer matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.

Monte Carlo Study of Planar Rotator Model with WeakDzyaloshinsky–Moriya Interaction

With the help of an improvement Monte Carlo method, theBerezinskii–Kosterlitz–Thouless phase transition arising intwo-dimensional planar rotator model with weakDzyaloshinsky–Moriya (DM) interaction is investigated. The effectsof the DM interaction on specific heat, susceptibility, andmagnetization are simulated. The critical temperature oftransitions is determined by the so-called Bindercumulant and the susceptibility of finite-size scaling. We findthat the chiral Z2 symmetry reduced by the DM interactionsplays an important role in a two-dimensional XY spin system,typically, the critical temperature is sensitive to weak DM spincouplings.

Kosterlitz-Thouless phase transition in microcavity polariton system

The Kosterlitz-Thouless phase transition in a system of exciton-polaritons in a microcavity is studied. The transition temperature to superfluid state was found as a function of exciton-photon detuning. A nonquadratic dispersion law was taken into account in the framework of the self-consistent harmonic approximation (SCHA).

New Monte Carlo Simulations to a Generalized XY Model

A new combination Monte Carlo (MC) technique of the classical Metropolisalgorithm and the Swendsen–Wang cluster algorithm is proposed.Upon application of the MC technique, the thermodynamic properties of ageneralized two-dimensional XY model with chiral Dzyaloshinski–Moriya(DM) interactions are simulated for various DM interactions. Thespecific heat, order parameter and the integrated correlation time aresimulated. We find that there exists a high-temperatureKosterlitz–Thouless-type phase transition related to strong DMspin chiralities. As the DM strength increases the critical temperatureof the Kosterlitz–Thouless phase transition increases. It is shown thatthe combination algorithm is faster than the Metropolis algorithms.

Hidden Caldeira-Leggett Dissipation in a Bose-Fermi Kondo Model

We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy-fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe physical quantities close to the quantum phase transition.

The two-dimensionalXYmodel at the transition temperature: a high-precision Monte Carlo study

We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature.

Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional (2D) Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D $XY$ model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.

Stability of indirect biexcitons in superlattices

The unstability of the ground state of the system of interacting two-dimensional indirect excitons in a slab of superlattice with alternating electron and hole layers is established. The stable system of indirect quasi-two-dimensional biexcitons, consisting from indirect excitons with opposite directed dipole moments is considered. The radius and the binding energy of indirect biexciton are calculated. Collective spectrum of low-density system of two-dimensional indirect biexcitons, interacting as electrical quadrupoles, is derived. The density of superfluid component n s( T) and the temperature of the Kosterlitz–Thouless phase transition to the superfluid state in this system are obtained. We assume there are no external fields applied to the slab of superlattice under consideration.