Thouless Transition Research Articles

Superfluid-Mott insulator and superfluid-charge density wave transitions in a one-dimensional Bose–Hubbard model

The superfluid to the Mott insulator transition is studied in the Bose–Hubbard model with contact interactions U at the density ρ=1, and at the half-filling ρ=1/2 added the next nearest interactions V which is responsible for the charge density wave (CDW). The Berezinski–Kosterlitz–Thouless transition is analyzed from the points of the dual Sine–Gordon model and the boson-spin equivalence by the conformal field theory. Eventually the prescription for the boson system is developed and the Mott insulator transition point and the superfluid to CDW transition point are estimated.

Percolation of interacting classical dimers on the square lattice

We study the percolation properties of the interacting classical dimer model on the square lattice by means of Monte Carlo simulations and finite-size scaling analysis. We define Ising clusters based on the dimer configuration; the percolation point of the clusters coincides with the critical point of the Kosterlitz–Thouless transition of the dimer model, which is Tc=0.654(2). Furthermore, we find that the largest cluster at the Kosterlitz–Thouless point is a fractal, with fractal dimension Dc=1.874(2), which coincides with the critical exponent describing the critical behavior of the dimer–dimer correlation function, which is theoretically predicted to be 15/8.

Superfluid phase transition in two-dimensional excitonic systems

We study the superfluid phase transition in the two-dimensional (2D) excitonic system. Employing the extended Falicov–Kimball model (EFKM) and considering the local quantum correlations in the system composed of conduction band electrons and valence band holes we demonstrate the existence of the excitonic insulator (EI) state in the system. We show that at very low temperatures, the particle phase stiffness in the pure-2D excitonic system, governed by the non-local cross correlations, is responsible for the vortex–antivortex binding phase-field state, known as the Berezinskii–Kosterlitz–Thouless (BKT) superfluid state. We demonstrate that the existence of excitonic insulator phase is a necessary prerequisite, leading to quasi-long-range order in the 2D excitonic system. • Excitonic superfluidity is studied in two-dimensional extended Falicov–Kimball model. • Correlations considers to derive the gap and phase-stiffness parameter. • The Berezinskii–Kosterlitz–Thouless transition critical temperature is calculated.

MONTE CARLO STUDY OF THE XY-MODEL ON SIERPIŃSKI CARPET

We have performed a Monte Carlo (MC) study of the classical XY-model on a Sierpiński carpet, which is a planar fractal structure with infinite order of ramification and fractal dimension 1.8928. We employed the Wolff cluster algorithm in our simulations and our results, in particular those for the susceptibility and the helicity modulus, indicate the absence of finite-temperature Berezinskii–Kosterlitz–Thouless (BKT) transition in this system.

Berezinskii—Kosterlitz—Thouless Transition in a Two-Dimensional Random-Bond XY Model on a Square Lattice

We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorders lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii—Kosterlitz—Thouless transition temperature decreases as the variance increases and the transition can even be destroyed as long as the disorder is strong enough.

Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model

In this paper we study the influence of the single-ion anisotropy in the two-dimensional biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. It is common to represent the bilinear and biquadratic terms by J1=Jcosθ and J2=Jsinθ, respectively, and the many phases present in the model as a function of θ are well documented. However we have adopted a constant value for the bilinear constant (J1=1) and small values of the biquadratic term (|J2|<J1). Specially, we have analyzed the quantum phase transition due to the single-ion anisotropic constant D. For values below a critical anisotropic constant Dc the energy spectrum is gapless and at low finite temperatures the order parameter correlation has an algebraic decay (quasi-long-range order). Moreover, in D<Dc phase there is a transition temperature where the quasi-long-range order (algebraic decay) is lost and the decay becomes exponential, similar to the Berezinski–Kosterlitz–Thouless (BKT) transition. For D>Dc, the excited states are gapped and there is no spin long-range order (LRO) even at zero temperature. Using Schwinger bosonic representation and Self-Consistent Harmonic Approximation (SCHA), we have studied the quantum and thermal phase transitions as a function of the bilinear and biquadratic constants.

Finite-size scaling method for the Berezinskii–Kosterlitz–Thouless transition

We test an improved finite-size scaling method for reliably extracting the critical temperature TBKT of a Berezinskii–Kosterlitz–Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness ρs at TBKT in combination with the Kosterlitz–Nelson relation between the transition temperature and the stiffness, ρs(TBKT) = 2TBKT/π, we define a size-dependent transition temperature TBKT(L1,L2) based on a pair of system sizes L1,L2, e.g., L2 = 2L1. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining TBKT(L1,L2). For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for L up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result TBKT = 0.8935(1) is several error bars above the previously best estimates of the transition temperature, TBKT ≈ 0.8929. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated TBKT because of the neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions.

Observation of superfluidity in two- and one-dimensions

Even though there is no long-range-ordered state of a superfluid in dimensions lower than the three-dimension (3D) such as bulk 4He liquid, superfluidity has been observed for flat 4He films in 2D and recently for nanotubes of 4He in 1D by the torsional oscillator method. In the 2D state, in addition to the superfluid below the 2D Kosterlitz–Thouless transition temperature TKT, superfluidity is also observed in a normal fluid state above TKT, which depends strongly on the measurement frequency and the system size. In the 1D state of the nanotubes, superfluidity is directly observed as a frequency shift in the torsional oscillator experiment. Some calculations suggest a superfluidity of a 1D Bose fluid with a finite length, where thermal excitations of 2π–phase winding play the main role for superfluid onset of each tube. Dynamics of the 1D superfluidity is also suggested by observing the dissipation in the torsional oscillator experiment.

Berezinskii–Kosterlitz–Thouless transition in two-dimensional arrays of Josephson coupled Bose–Einstein condensates

Abstract We study the phase transition occurring in Bose–Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii–Kosterlitz–Thouless transition at a finite temperature T KT to the ordered state composed of bound vortex–antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature T KT . Finally, we discuss the results in the context of system parameters and possible experiments.

Evidence for Berezinskii–Kosterlitz–Thouless transition in atomically flat two-dimensional Pb superconducting films

We report results from scanning tunneling microscopy and transport measurements on a series of crystalline lead films containing an integer number of atomic layers, and find that the observed features in sufficiently thin films are consistent with Berezinskii–Kosterlitz–Thouless (BKT) physics. Specifically, Cooper pairing and superconductivity disappear at two distinct temperatures; the current–voltage characteristics in the intermediate phase are non-Ohmic; and the temperature and current dependences of resistance agree with the expectation from the BKT theory.

Phase diagram of ferromagnetic XY model with nematic coupling on a triangular lattice

The phase diagram of a ferromagnetic XY model with a nematic coupling (coupling strength x) on a triangular lattice is studied by means of Monte Carlo simulation. The algebraic-magnetic order associated with Kosterlitz–Thouless (KT) transition is observed over the whole x range. In the large x region, the phase transition from the algebraic-magnetic order to the algebraic-nematic order occurs at TI. In addition, this phase transition can be scaled with the two-dimensional Ising critical exponents, demonstrating that the present system belongs to the universality class of Ising transition at TI.

Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold

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 L × L , from 16 L 640 . 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, p c (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as T BKT ∝ ( p − p c ) 0.908 and the specific heat behaves as T s h ∝ p 1.133 .

Kosterlitz–Thouless transition in disordered two-dimensional topological insulators

The disorder-driven metal–insulator transition in the quantum spin Hall systems is studied by scaling analysis of the Thouless conductance g. Below a critical disorder strength, the conductance is independent of the sample size M, an indication of critically delocalized electron states. The calculated beta function β = dlng/dlnM indicates that the metal–insulator transition is of Kosterlitz–Thouless (KT) type, which is characterized by binding and unbinding of vortex–antivortex pairs of the local currents. The KT-like metal–insulator transition is a basic characteristic of the quantum spin Hall state, being independent of the time-reversal symmetry.

Superinsulator–superconductor duality in two dimensions

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.

Magnetic charge and ordering in kagome spin ice

We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbours, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz-Thouless (KT) transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high- and low-temperature phase transitions are of the Ising and 3-state Potts universality classes, respectively. Freeze-out of defects in the charge order produce a very large spin correlation length in the intermediate phase. As a result of that, the lower-temperature transition appears to be of the KT type.

Emergent magnetic monopoles in frustrated magnetic systems

Emergent magnetic monopoles in frustrated magnetic systems

Large-Scale Monte Carlo Simulation of Two-Dimensional Classical XY Model Using Multiple GPUs

We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L =65536, we investigate the Kosterlitz–Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature β KT is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, -2 r , and precisely reproduce the theoretical prediction -2 r =1/8.

Dimensional crossover transition in a system of weakly coupled superconducting nanowires

Owing to recent observations of superconductivity in quasi-one-dimensional (1D) systems, Josephson arrays composed of aligned and weakly coupled 1D superconducting nanowires have attracted renewed interest for modeling the experimental data. Carrying out Monte Carlo simulations, we go beyond the traditional mean field results to show that the competition between 1D fluctuations and the transverse Josephson coupling between the nanowires can lead to a 1D–3D crossover transition at a temperature Tc below the mean field TCO of the wires, with interesting and surprising pre-transitional characteristics. In particular, the specific heat exhibits a rounded peak between Tc and TCO, and the phase correlation length within the transverse ab plane diverges at Tc from above, in a manner consistent with that of a 2D Berezinskii–Kosterlitz–Thouless transition. Simultaneous with the above, quenching of phase fluctuations along the c-axis of the wires is also seen to occur at Tc. These behaviors are in excellent agreement with the experimental manifestations observed in the superconductivity of 4 Å carbon nanotubes.

Excitonic condensation for the surface states of topological insulator bilayers

We propose a generic topological insulator bilayer (TIB) system to study the excitonic condensation with self-consistent mean-field (SCMF) theory. We show that the TIB system presents the crossover behavior from the Bardeen–Cooper–Schrieffer (BCS) limit to the Bose–Einstein condensation (BEC) limit. Moreover, in comparison with traditional semiconductor systems, we find that for the present system the superfluid property in the BEC phase is more sensitive to electron–hole density imbalance and the BCS phase is more robust. Applying this TIB model to the Bi2Se3-family material, we find that the BEC phase is most likely to be observed in experiment. We also calculate the critical temperature for the Bi2Se3-family TIB system, which is ∼100 K. More interestingly, one can expect this relative high-temperature excitonic condensation, since our calculated SCMF critical temperature is approximately equal to the Kosterlitz–Thouless transition temperature.

Critical behavior of the two-dimensional fully frustrated XY model

Critical behavior of the two-dimensional fully frustrated XY model has been investigated with Monte Carlo methods. Based on the dynamic scaling ansatz of the magnetization for temperatures above the transition temperature, the correlating time, spatial correlation length has been extracted. Fitting the correlation length to the exponential singularity assumed for the Kosterlitz–Thouless (KT) transition, the transition temperature TKT and the static exponent ν have been determined. The TKT = 0.45065(3) is one percent or two higher than that estimated from simulations in equilibrium. Moreover, the exponent ν = 0.089(2) is smaller than the theoretical value 0.5.