Berezinskii-Kosterlitz-Thouless Phase Research Articles

Probing Berezinskii–Kosterlitz–Thouless Phase Transition of Spin-Half XXZ Chain by Quantum Fisher Information* *Supported by the National Natural Science Foundation of China under Grant Nos. 11065005 and 11365006, and the Innovation Team Foundation of the Education Department of Guizhou Province under Grant No. [2014]35

The Berezinskii–Kosterlitz–Thouless phase transition of spin-1/2 XXZ chain is reinvestigated by the quantum Fisher information. Quantum Fisher informations of the whole N sites and the partial N/3 sites display remarkably similar behaviors near the critical point. The critical exponent of quantum Fisher information is obtained as β = 0.47, which is consistent with the results obtained by the concurrence and quantum discord.

DMRG study of the Berezinskii–Kosterlitz–Thouless transitions of the 2D five-state clock model

The two Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus ϒ2 is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with σ = 1/2 at the two transitions. The predicted universal values of ϒ2 are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature BKT transition, like the XY model, and shown to take a new universal value at the low-temperature BKT transition. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with η = 1/4.

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.

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.

Quasi Long Range Order of Defects in Frustrated Antiferromagnetic Ising Models on Spatially Anisotropic Triangular Lattices

It is known that there is no phase transition down to zero temperature in the antiferromagnetic Ising model on spatially anisotropic triangular lattices, in which the exchange coupling of one direction is stronger than those of other two directions. In the model, the low-temperature physics is governed by domain-wall excitations (defects) residing on bonds of the strong-coupling direction. In this letter, we show that an additional small attractive interaction between defects (a ferromagnetic next-nearest-neighbor interaction in the weak-coupling direction) leads to a Berezinskii-Kosterlitz-Thouless (BKT) transition at a finite temperature, by performing the Monte Carlo simulation. The BKT phase can be viewed as the phase with a quasi long-range order of defects. We determine the phase diagram in a wide parameter regime and argue the phase structure from statistical-mechanics and field-theory viewpoints.

Phase transitions in a triangular Blume-Capel antiferromagnet

We study the critical behavior of a frustrated Blume-Capel (BC) antiferromagnet on a triangular lattice by Monte Carlo simulations. For a reduced single-ion anisotropy strength $\ensuremath{-}1.47\ensuremath{\lesssim}\ensuremath{\Delta}<0$, we find two phase transitions. The low-temperature phase is characterized by the antiferromagnetic long-range ordering (LRO) on two sublattices with the third one remaining in a nonmagnetic state. At higher temperatures, there is a critical region of the Berezinskii-Kosterlitz-Thouless (BKT) type with a power-law decaying spin-correlation function. For $\ensuremath{-}1.5\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\lesssim}\ensuremath{-}1.47$, there is only one phase transition from the LRO to the paramagnetic region and the transition is of first order. The presence of the BKT phase in the current frustrated BC model is a new feature not observed in its nonfrustrated counterparts. The values of the decay exponent $\ensuremath{\eta}$ of the BKT phase corresponding to upper and lower temperatures appear to be consistent with the theoretical predictions for the six-state clock model.

Observation of scale invariance and universality in two-dimensional Bose gases

The collective behaviour of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics; for example, thermodynamic observables follow generalized scaling laws near the phase transition. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry result in a broad fluctuation regime and an extended range of universal scaling behaviour. Studies of the BKT transition in cold atoms have stimulated great interest in recent years, but a clear demonstration of critical behaviour near the phase transition has remained elusive. Here we report in situ density and density-fluctuation measurements of two-dimensional Bose gases of caesium at different temperatures and interaction strengths, observing scale-invariant, universal behaviours. The extracted thermodynamic functions confirm the existence of a wide universal region near the BKT phase transition, and provide a sensitive test of the universality predicted by classical-field theory and quantum Monte Carlo calculations. Our experimental results provide evidence for growing density-density correlations in the fluctuation region, and call for further explorations of universal phenomena in classical and quantum critical physics.

Berezinskii-Kosterlitz-Thouless transition uncovered by the fidelity susceptibility in theXXZmodel

We investigate the one-dimensional Heisenberg $\mathit{XXZ}$ model involving the Dzyaloshinskii-Moriya (DM) interaction from the viewpoint of quantum information. By using the density-matrix--renormalization-group technique, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the ground-state fidelity, the fidelity susceptibility, and the entanglement entropy. We argue that the BKT phase transition can be well characterized in our model, and the critical line induced by the DM interaction can also be detected.

The Berezinskii–Kosterlitz–Thouless transition in imbalanced 2D Fermi gases: The role of fluctuations

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.

Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized [formula omitted] model

The Berezinskii–Kosterlitz–Thouless (BKT) phase transition of 2D dilute generalized X Y model on a triangular lattice is studied by a hybrid Monte Carlo (MC) method. The critical temperatures are obtained by several methods for dilute and non-dilute cases. It is found that the critical temperature decreases with increasing non-magnetic occupation density ρ and the BKT phase transition vanishes when the magnetic occupation density reaches the site percolation threshold: ρ m a g = p c = 0.5 . Some thermodynamic quantities are also discussed.

Berezinskii-Kosterlitz-Thouless phase transition for the dilute planar rotator model on a triangular lattice

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition for the dilute planar rotator model on a triangular lattice is studied by using a hybrid Monte Carlo method. The phase-transition temperatures for different nonmagnetic impurity densities are obtained by three approaches: finite-size scaling of plane magnetic susceptibility, helicity modulus, and Binder's fourth cumulant. It is found that the phase-transition temperature decreases with increasing impurity density {rho} and the BKT phase transition vanishes when the magnetic occupancy falls to the site percolation threshold: 1-{rho}{sub c}=p{sub c}=0.5.

BKT phase in systems of spinless strongly interacting one-dimensional fermions

We present the ground-state wavefunctions for a system of spinless one-dimensional fermions in the limit of an infinitely strong interaction, and we demonstrate explicitly that the system symmetry is lower than the original symmetry of the Hamiltonian. As a result, the system in this limit undergoes a second-order phase transition into a phase with finite density of chiral pairs. The phase transforms continuously into a Berezinskii-Kosterlitz-Thouless (BKT) phase if the interaction in the model decreases. Therefore, just the BKT phase is realized in nature. The temperature of the smearing phase transition is calculated.

Josephson vortex lattice melting in Bi-2212 probed by commensurate oscillations of Josephson flux-flow

We studied the commensurate semi-fluxon oscillations of Josephson flux-flow (JFF) in a Bi-2212 stacked structures near $T_c$ as a probe of melting of Josephson vortex lattice (JVL). We found that oscillations exist above 0.5T. The amplitude of oscillations is found to decrease gradually with temperature and to turn to zero without any jump at $T=T_0$, 3.5K below the resistive transition temperature $T_c$ indicating the phase transition of the second order. This characteristic temperature $T_0$ is identified as the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, $T_{BKT}$, in elementary superconducting layers of Bi-2212 at zero magnetic field. On the base of these facts we infer that melting of triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and anti-vortices. The $B-T$ phase diagram of the BKT phase found out from our experiment is consistent with theoretical predictions.

Transition from the Bose–Einstein condensate to the Berezinskii–Kosterlitz–Thouless phase

We obtain a phase diagram for a trapped two-dimensional ultracold Bose gas. We find a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose–Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose–Einstein condensate, a vortex pair plasma with a fluctuating condensate phase, and a thermal Bose gas. The existence of the vortex pair phase could be verified using current experimental set-ups.

Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model

We study the two-dimensional attractive Hubbard model using the mapping onto the half-filled repulsive Hubbard model in a uniform magnetic field coupled to the fermion spins. The low-energy effective action for charge and pairing fluctuations is obtained in the hydrodynamic regime. We recover the action of a Bose superfluid where half the fermion density is identified as the conjugate variable of the phase of the superconducting order parameter. By integrating out charge fluctuations, we obtain a phase-only action. In the zero-temperature superconducting state, this action describes a collective phase mode smoothly evolving from the Anderson-Bogoliubov mode at weak coupling to the Bogoliubov mode of a Bose superfluid at strong coupling. At finite temperature, the phase-only action can be used to extract an effective XY model and thus obtain the Berezinskii-Kosterlitz-Thouless (BKT) phase transition temperature. We also identify a renormalized classical regime of superconducting fluctuations above the BKT phase transition, and a regime of incoherent pairs at higher temperature. Special care is devoted to the nearly half-filled case where the symmetry of the order parameter is enlarged to SO(3) due to strong ${\bf q}=(\pi,\pi)$ charge fluctuations. The low-energy effective action is then an SO(3) non-linear sigma model with a (symmetry breaking) magnetic field proportional to the doping. In the strong-coupling limit, the attractive Hubbard model can be mapped onto the Heisenberg model, from which we recover the Gross-Pitaevskii equation in the low-density limit.

Breaking-symmetry fields in two-dimensional planar models

The planar model in presence of symmetry-breaking fields is studied on square and triangular lattices by Monte Carlo simulation. In the square model a phase transition with non-universal critical exponents is found. In the triangular lattice a Berezinskii–Kosterlitz–Thouless phase is observed over a finite temperature region between the low-temperature ordered phase and the high-temperature paramagnetic phase.

Breaking-symmetry fields in two-dimensional planar models

Abstract The planar model in presence of symmetry-breaking fields is studied on square and triangular lattices by Monte Carlo simulation. In the square model a phase transition with non-universal critical exponents is found. In the triangular lattice a Berezinskii–Kosterlitz–Thouless phase is observed over a finite temperature region between the low-temperature ordered phase and the high-temperature paramagnetic phase.

Quantum Monte Carlo simulation of two-dimensional S=1/2 antiferromagnets with very weak easy-plane anisotropy

We study the critical and thermodynamic properties of an S=1/2 two-dimensional quantum XXZ antiferromagnet with weak easy-plane anisotropy using the continuous-time quantum Monte Carlo method based on the loop-cluster algorithm. A detailed finite-size scaling analysis reveals that the model displays a finite temperature Berezinskii–Kosterlitz–Thouless (BKT) transition for anisotropy as small as 10−3, the dominant isotropic coupling. For larger anisotropy (10−2) we single out relevant features of anisotropic behavior that anticipate the BKT transition. Implications for experimental observation of a BKT phase in real magnets are discussed.

2D ferromagnetic models with symmetry-breaking interactions: self-consistent harmonic approximation

The 2D classical planar rotator, XY and Heisenberg ferromagnetic models with uniaxial in-plane anisotropy are investigated using self-consistent harmonic approximation. We found that for sufficiently large anisotropy there is implemented the phase transition from ferromagnetic phase into paramagnetic one. We also determine the range of anisotropy values for which the XY and planar rotator models undergo phase transition in temperature from the state with long-range magnetic order into Berezinskii–Kosterlitz–Thouless phase with topological order. The same calculations are carried out for the models with magnetoelastic coupling.

Phase transitions in the quantum easy-plane antiferromagnet on the triangular lattice

The quantum effects on the thermodynamics of the easy-plane triangular antiferromagnet, displaying classically both an Ising and a Berezinskii–Kosterlitz–Thouless phase transition, are evaluated by means of the pure-quantum self-consistent harmonic approximation, which allows one to deal with any spin value through classical Monte Carlo simulations. Data for the specific heat, the static spin correlation functions, and the in-plane correlation length are presented in a broad range of temperatures, for different values of the spin and of the exchange anisotropy. Our results for the quantum transition temperatures are in good agreement with the few available theoretical and numerical estimates.