Berezinskii-Kosterlitz-Thouless Research Articles

Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects

We perform a detailed finite-size scaling analysis of the sheet resistance in Bi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface in the presence and absence of a magnetic field applied perpendicular to the system. Our main aim is to explore the occurrence of Berezinskii-Kosterlitz-Thouless (BKT) and quantum phase transition behavior in the presence of limited size, stemming from the finite extent of the homogeneous domains or the magnetic field. Moreover we explore the implications thereof. Above an extrapolated BKT transition temperature, modulated by the thickness $d$, gate voltage $%V_{g}$ or magnetic field $H$, we identify a temperature range where BKT behavior occurs. Its range is controlled by the relevant limiting lengths,which are set by the extent of the homogeneous domains or the magnetic field. The extrapolated BKT transition lines $T_{c}\left(d,V_{g},H\right) $ uncover compatibility with the occurrence of a quantum phase transition where $T_{c}\left( d_{c},V_{gc},H_{c}\right) =0$. However, an essential implication of the respective limiting length is that the extrapolated phase transition lines $T_{c}\left( d,V_{g},H\right) $ are unattainable. Consequently, given a finite limiting length, BKT and quantum phase transitions do not occur. Nevertheless, BKT and quantum critical behavior is observable, controlled by the extent of the relevant limiting length. Additional results and implications include: the magnetic field induced finite size effect generates a flattening out of the sheet resistance in the $T\rightarrow 0$ limit, while in zero field it exhibits a characteristic temperature dependence and vanishes at $T=0$ only. The former prediction is confirmed in both, the Bi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface, as well as in previous studies. The latter is consistent with the LaAlO$_{3}$/SrTiO$_{3}$ interface data, while the Bi-films exhibit a flattening out.

Antiferromagnetic triangular Blume-Capel model with hard-core exclusions.

Using Monte Carlo simulation, we analyze phase transitions of two antiferromagnetic (AFM) triangular Blume-Capel (BC) models with AFM interactions between third-nearest neighbors. One model has hard-core exclusions between the nearest-neighbor (1NN) particles (3NN1 model) and the other has them between the nearest-neighbor and next-nearest-neighbor particles (3NN12 model). Finite-size scaling analysis reveals that in these models, the transition from the paramagnetic to long-range order (LRO) AFM phase is either of the first order or goes through an intermediate phase which might be attributed to the Berezinskii-Kosterlitz-Thouless (BKT) type. The properties of the low-temperature phase transition to the AFM phase of the 1NN, 3NN1, and 3NN12 models are found to be very similar for almost all values of a normalized single-ion anisotropy parameter, 0 < δ < 1.5. Higher temperature behavior of the 3NN12 and 3NN1 models is rather different from that of the 1NN model. Three phase transitions are observed for the 3NN12 model: from the paramagnetic phase to the phase with domains of the LRO AFM phase at T(c), from this structure to the diluted frustrated BKT-type phase at T(2), and from the frustrated phase to the AFM LRO phase at T(1). For the 3NN12 model, T(c) > T(2) > T(1) at 0 < δ < 1.15 (range I), T(c) ≈ T(2) > T(1) at 1.15 < δ < 1.3 (range II), and T(c) = T(2) = T(1) at 1.3 < δ < 1.5 (range III). For the 3NN1 model, T(c) ≈ T(2) > T(1) at 0 < δ < 1.2 (range II) and T(c) = T(2) = T(1) at 1.2 < δ < 1.5 (range III). There is only one first-order phase transition in range III. The transition at T(c) is of the first order in range II and either of a weak first order or a second order in range I.

The Depinning Transition in Presence of Disorder: A Toy Model

We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability distribution of a single real variable. For this toy model, the critical line is known exactly in one particular case and it can be calculated perturbatively in the general case. One can also show that, at the transition, there is no fixed distribution accessible by renormalization which corresponds to a disordered fixed point. Instead, both our numerical and analytic approaches indicate a transition of infinite order (of the Berezinskii–Kosterlitz–Thouless type). We give numerical evidence that this infinite order transition persists for the problem of the depinning transition with disorder on the hierarchical lattice.

Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases

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.

Universality of the Berezinskii–Kosterlitz–Thouless type of phase transition in the dipolar XY-model

We investigate the nature of the phase transition occurring in a planar XY-model spin system with dipole–dipole interactions. It is demonstrated that a Berezinskii–Kosterlitz–Thouless (BKT) type of phase transition always takes place at a finite temperature separating the ordered (ferro) and the disordered (para) phases. The low-temperature phase corresponds to an ordered state with thermal fluctuations, composed of a ‘gas’ of bound vortex–antivortex pairs, which would, when considered isolated, be characterized by a constant vortex–antivortex attraction force which is due to the dipolar interaction term in the Hamiltonian. Using a topological charge model, we show that small bound pairs are easily polarized, and screen the vortex–antivortex interaction in sufficiently large pairs. Screening changes the linear attraction potential of vortices to a logarithmic one, and leads to the familiar pair dissociation mechanism of the BKT type phase transition. The topological charge model is confirmed by numerical simulations, in which we demonstrate that the transition temperature slightly increases when compared with the BKT result for short-range interactions.

Entanglement spectrum and quantum phase transitions in one-dimensional [formula omitted] XXZ model with uniaxial single-ion anisotropy

Quantum phase transitions (QPTs) in one-dimensional S=1 XXZ model with uniaxial single-ion anisotropy are investigated. Bipartite entanglement, entanglement spectrum, and Schmidt gap are found to be capable of describing all the QPTs, even the infinite-order Berezinskii–Kosterlitz–Thouless (BKT) transition. According to the singular behavior of the second-order derivative of ground-state energy, the QPT between XY2 and antiferromagnetic phases is a second-order but not a BKT transition. Energy level crossing, accompanied with discontinuous entanglement entropy and entanglement spectrum, is observed at the transition point between the large-D and antiferromagnetic phases, therefore it should be a first-order QPT. In addition, doubly degenerate entanglement spectrum in the Haldane phase is observed.

Kosterlitz-Thouless Transition: The Diluted XY model

The effect of nonmagnetic disorder on Berezinskii-Kosterlitz-Thouless (BKT) transition in the two-dimensional ferromagnetic XY model on a square lattice, diluted by randomly placed vacancies can be an important source of information on the role played by vortexes in this transition. The transition temperature TBKT is determined as a function of vacancy density ρv by stiffness ρ and for different size of the lattice. The anomalous behavior for TBKT when ρv is close to the square lattice percolation limit is a consequence of the effect of finite size of lattice and not due the quantum fluctuations as concluded in literature. We obtain that TBKT falls to zero at ρv ≈ 0.40 close to the value 0.41 obtained for the classic model.

A scheme to observe universal breathing mode and Berezinskii–Kosterlitz–Thouless phase transition in a two-dimensional photon gas

A system of two-dimensional photon gas has recently been realized experimentally. We show that this setup can be used to observe a universal breathing mode of photon gas and a modification in the experimental setup would open up a possibility of observing the Berezinskii–Kosterlitz–Thouless (BKT) phase transition in such a system. Furthermore, the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.

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.

Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases

We study the superfluid properties of two-dimensional spin-population-imbalanced Fermi gases to explore the interplay between the Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible instability towards the Fulde-Ferrell (FF) state. By the mean-field approximation together with quantum fluctuations, we obtain phase diagrams as functions of temperature, chemical potential imbalance, and binding energy. We find that the fluctuations change the mean-field phase diagram significantly. We also address possible effects of the phase separation and/or the anisotropic FF phase to the BKT mechanism. The superfluid density tensor of the FF state is obtained, and its transverse component is found always vanishing. This causes divergent fluctuations and possibly precludes the existence of the FF state at any nonzero temperature.

Quantum phase transition of light in coupled optical cavity arrays: A renormalization group study

We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons. We predict the quantum phase transition between the photonic Coulomb blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations. The renormalization group equation shows explicitly that for this system there is no self-duality. The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system. The presence of single Rabi frequency oscillation in the system leads to the BKT transition where system shows the quantum phase transition from photonic metallic state to the Coulomb blocked induced insulating phase. For the other BKT transition when the z-component of exchange interaction is absent, the system shows the transition from the photonic metallic state to the photonic superfluid phase. We also predict the commensurate to incommensurate transition under the laser field detuning.

Effect of amplitude fluctuations on the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a generic transition describing the loss of coherence in two-dimensional systems and has been invoked, for example, to describe the superconductor-insulator transition in thin films. However, recent experiments have shown that the BKT transition, driven by phase fluctuations, is not sufficient to describe the loss of superconducting order, and amplitude fluctuations must also be taken into account. The standard models that are extensively used to model two-dimensional superconductors are the Hubbard and $\mathit{XY}$ models. Whereas the $\mathit{XY}$ model allows only phase fluctuations, the Hubbard model has an extra degree of freedom: amplitude fluctuations. In this paper we compare two Hubbard models with the same critical temperature but with different interactions and deduce the role of the amplitude fluctuations in the superconducting transition. For this purpose, a novel approximation is presented and used. We derive an effective phase-only ($\mathit{XY}$) Hamiltonian, incorporating amplitude fluctuations in an explicit temperature dependence of the phase rigidity. We study the relation between amplitude fluctuations and coupling strength. Our results support existing claims about the suppression of phase rigidity due to amplitude fluctuations not present in the $\mathit{XY}$ model.

Correlated Conductance Fluctuations Close to the Berezinskii-Kosterlitz-Thouless Transition in Ultrathin NbN Films

We probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultrathin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depends strongly on the roughness and structural inhomogeneity of the superconducting films. Our experiment outlines a novel fluctuation-based kinetic probe in detecting the nature of superconductivity in disordered low-dimensional materials.

Turbulence in the two-dimensional Fourier-truncated Gross–Pitaevskii equation

We undertake a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross–Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. Firstly, there are transients that depend on the initial conditions. In the second regime, power-law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii–Kosterlitz–Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other.

Spin-polarized hydrogen and its isotopes: A rich class of quantum phases (Review Article)

We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.

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.

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.

Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions

We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size L, and not as powers of 1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.