Kosterlitz-Thouless Phase Transition Research Articles

An exactly solvable model of randomly pinned charge density waves in two dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

Fazovye perekhody v chasovoy modeli s chislom sostoyaniy spina <i>q </i>= 5 na treugol'noy reshetke

The phase transitions and thermodynamic properties of the clock model with q = 5 spin states on a triangular lattice have been investigated using the Wang–Landau Monte Carlo algorithm. The phase transitions have been analyzed with the histogram method and the fourth-order Binder cumulant method. Two Berezinskii–Kosterlitz–Thouless phase transitions are shown to be observed in the ferromagnetic clock model, while a second-order phase transition has been detected in the antiferromagnetic clock model.

Flux-flow instability across Berezinskii Kosterlitz Thouless phase transition in KTaO3 (111) based superconductor

The nature of energy dissipation in 2D superconductors under perpendicular magnetic field at small current excitations has been extensively studied over the past two decades. However, dissipation mechanisms at high current drives remain largely unexplored. Here we report on the distinct behavior of energy dissipation in the AlOx/KTaO3 (111) system hosting 2D superconductivity in the intermediate disorder regime. The results show that below the Berezinskii Kosterlitz Thouless (BKT) phase transition temperature (TBKT), hot-spots and Larkin Ovchinnikov type flux-flow instability (FFI) are the major channels of dissipation, leading to pronounced voltage instability at large currents. Furthermore, such FFI leads to a rare observation of clockwise hysteresis in current-voltage characteristics within the temperature range TBKT < T < TC (TC is superconducting transition temperature). These findings deepen our understanding of how a BKT system ultimately transforms to a normal state under increasing current.

Two Types of Topological Kosterlitz–Thouless Phase Transitions in SmMnO3+δ Manganites, Driven by External Magnetic Field

Two Types of Topological Kosterlitz–Thouless Phase Transitions in SmMnO3+δ Manganites, Driven by External Magnetic Field

Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition

Entanglement is known as an important indicator for characterizing different types of quantum phase transitions (QPTs), however it faces some challenges in the Kosterlitz-Thouless (KT) phase transitions due to an essential singularity which cannot be identified in finite derivatives of the ground state energy. In this paper, we consider global entanglement (GE) in a KT phase transition and show that while it does not indicate any clear signature of the phase transition, the conditional version of GE is a good indicator with strong signatures of the KT transition. In particular, we study a deformed version of the $Z_d$ Kitaev model which has an intermediate KT phase which separates a $Z_d$ topological phase from a magnetized phase at two different KT transition points. Using a mapping to the classical $d$-state clock model, we consider GE and the generalized GE and show that they do not provide a reliable indicator of transition points. However, their difference called conditional global entanglement (Q) shows a peak at the first KT transition point. Additionally, we show that it can characterize various phases of the model as it behaves substantially different in each phase. We therefore conclude that Q is a useful measure that can characterize various phases of KT QPTs as well as their related critical points.

An Elementary Proof of Phase Transition in the Planar XY Model

Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fröhlich and Spencer (Commun Math Phys 81(4):527–602, 1981) and establishes a Berezinskii–Kosterlitz–Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers (Probab Relat Fields, 2021) on delocalisation of general integer-valued height functions, and classical correlation inequalities.

Binder ratio in the two-dimensional q-state clock model.

We study phase transition properties of the two-dimensional q-state clock model by an extensive Monte Carlo simulation. By analyzing the Binder ratio and its temperature derivative, we confirm that the two-dimensional q-state clock model exhibits two distinct Kosterlitz-Thouless phase transitions for q=5,6 but it has one second-order phase transition for q=4. The critical temperatures are estimated quite accurately from the crossing behavior of the Binder ratio (for q<5) and from negative divergent dips of the derivative of the Binder ratio (for q≥5) around these critical points. We also calculate the correlation length, the helicity modulus, and the derivative of the helicity modulus, and analyze their behaviors in different phases in detail.

Rapid detection of phase transitions from Monte Carlo samples before equilibrium

We found that Bidirectional LSTM and Transformer can classify different phases of condensed matter models and determine the phase transition points by learning features in the Monte Carlo raw data before equilibrium. Our method can significantly reduce the time and computational resources required for probing phase transitions as compared to the conventional Monte Carlo simulation. We also provide evidence that the method is robust and the performance of the deep learning model is insensitive to the type of input data (we tested spin configurations of classical models and green functions of a quantum model), and it also performs well in detecting Kosterlitz-Thouless phase transitions.

Unveiling quantum entanglement and correlation of sub-Ohmic and Ohmic baths for quantum phase transitions in dissipative systems

By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic case is identified, quite different from that in the sub-Ohmic regime. In a two-spin model, two distinct behaviors of the quantum discord are uncovered: one is related to the quantum entanglement between two spins and the other is decided by the correlation function in the position space rather than the entanglement.

Superradiant phase transitions in one-dimensional correlated Fermi gases with cavity-induced umklapp scattering

The phase transitions of one dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wavenumber equals two times of Fermi wavenumber, are studied with the bosonization and renormalization group (RG) techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted non-local interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then linked to the Kosterlitz-Thouless (KT) phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by infinitely small atom-cavity coupling strength, is preserved for any non-attractive local interactions. The phase transition occurs at finite critical coupling strength for attractive local interactions. Nevertheless, the critical dimension of the KT phase transition is also 2 like that in an ordinary local SG model. Our work provides an analytical framework for understanding the phase transitions in correlated intra-cavity Fermi gases.

Berezinskii–Kosterlitz–Thouless transition – A universal neural network study with benchmarks

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional (2D) classical XY and the 2D generalized classical XY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.

Scaling theory of the Kosterlitz-Thouless phase transition

We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. Relaxation times of both a normal power-law and an anomalous power-law with a logarithmic factor are studied. Finite-size and finite-entanglement scaling forms somehow similar to but different from a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived, and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be 0.302(1) at the infinite bond dimension on the basis of the scaling theories.

Magnetic order in XY-type antiferromagnetic monolayer CoPS3 revealed by Raman spectroscopy

Mermin-Wagner-Coleman theorem predicts no long-range magnetic order at finite temperature in the two-dimensional (2D) isotropic systems, but it does predict a quasi-long-range order with a divergent correlation length at the Kosterlitz-Thouless (KT) transition for planar magnets. As a representative of two-dimensional planar antiferromagnets, single-layer ${\mathrm{CoPS}}_{3}$ carries the promise of monolayer antiferromagnetic platforms for the ultimately thin spintronics. Here, with the aid of magnetostriction which is sensitive to the local magnetic order, we observe the signature phonon mode splitting of below ${T}_{\mathrm{KT}}$ in monolayer ${\mathrm{CoPS}}_{3}$. The two-magnon signal in the monolayer one manifests the associated magnetic transition. It indicates the quasi-long-range order in an exact 2D planar spin model below KT phase transition. The ratio ($J$\ensuremath{'}/$J$) between the interlayer and intralayer interactions, which characterizes the 2D behaviors, is evaluated to be around 0.03. Our results provide an efficient method to detect the quasi-long-range antiferromagnetic ordering in the two-dimensional magnets down to the monolayer limit.

Topologically induced metastability in a periodic XY chain

Non-trivial topological behavior appears in many different contexts in statistical physics, perhaps the most known one being the Kosterlitz–Thouless phase transition in the two-dimensional XY model. We study the behavior of a simpler, one dimensional, XY chain with periodic boundary and strong interactions, but rather than concentrating on the equilibrium measure, we try to understand its dynamics. The equivalent of the Kosterlitz–Thouless transition in this one-dimensional case happens when the interaction strength scales like the size of system N, yet we show that a sharp transition for the dynamics occurs at the scale of log N. When the interactions are weaker than a certain threshold, topological phases could not be observed over long times, while for interactions that are stronger than that threshold, topological phases become metastable, surviving for diverging time scales.

From hard spheres to hard-core spins

A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low density phase is liquid, while the high density phase is crystalline, an example of "order by disorder" as it is driven purely by entropic considerations. Here we study a family of hard spin models, which we call hardcore spin models, where we replace the translational degrees of freedom of hard spheres with the orientational degrees of freedom of lattice spins. Their hardcore interaction serves analogously to divide configurations of the many spin system into allowed and disallowed sectors. We present detailed results on the square lattice in $d=2$ for a set of models with $\mathbb{Z}_n$ symmetry, which generalize Potts models, and their $U(1)$ limits, for ferromagnetic and antiferromagnetic senses of the interaction, which we refer to as exclusion and inclusion models. As the exclusion/inclusion angles are varied, we find a Kosterlitz-Thouless phase transition between a disordered phase and an ordered phase with quasi-long-ranged order, which is the form order by disorder takes in these systems. These results follow from a set of height representations, an ergodic cluster algorithm, and transfer matrix calculations.

Geometrical and topological study of the Kosterlitz–Thouless phase transition in the XY model in two dimensions

Phase transitions do not necessarily correspond to a symmetry-breaking phenomenon. This is the case of the Kosterlitz–Thouless (KT) phase transition in a two-dimensional classical XY model, a typical example of a transition stemming from a deeper phenomenon than a symmetry-breaking. Actually, the KT transition is a paradigmatic example of the successful application of topological concepts to the study of phase transition phenomena in the absence of an order parameter. Topology conceptually enters through the meaning of defects in real space. In the present work, the same kind of KT phase transition in a two-dimensional classical XY model is tackled by resorting again to a topological viewpoint, however focussed on the energy level sets in phase space rather than on topological defects in real space. Also from this point of view, the origin of the KT transition can be attributed to a topological phenomenon. In fact, the transition is detected through peculiar geometrical changes of the energy level sets which, after a theorem in differential topology, are direct probes of topological changes of these level sets.

Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

AbstractThis paper focuses on the ground state phase diagram of a 1D spin‐1/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both numerically and analytically, some evidence is provided to clarify the identification of the ground state phase diagram. Local quantum correlations play a crucial role in detecting the critical lines either revealed or hidden by symmetry‐breaking. A non‐symmetry‐breaking disorder transition line can be identified by the first derivative of both entanglement of formation and quantum discord between nearest neighbour spins. In addition, the quantum correlations between the second neighbour spins can also be used to reveal Kosterlitz–Thouless phase transition when their interaction strength grows and becomes closer to the first nearest neighbour one. The results obtained using the Jordan–Wigner transformation confirm the accuracy of the numerical case.

Superfluidity of dipolar excitons in doped double-layered hexagonal lattice in a strong magnetic field

We predict the occurrence of Bose-Einstein condensation and superfluidity of dipolar magnetoexcitons for a pair of quasi-two-dimensional spatially separated $\alpha$-${\cal T}_3$ layers. We have solved a two-body problem for an electron and a hole for the model Hamiltonian for the $\alpha$-${\cal T}_3$ double layer in a magnetic field. The energy dispersion of collective excitations, the spectrum of sound velocity, and the effective magnetic mass of magnetoexcitons are obtained in the integer quantum Hall regime for high magnetic fields. The superfluid density and the temperature of the Kosterlitz-Thouless phase transition are probed as functions of the excitonic density, magnetic field, and the inter-layer separation.

Influence of Topological Phase Transition on Entanglement in the Spin-1 Antiferromagnetic XX Model in Two Dimensions

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 $$D_\mathrm{c}$$ . One discusses the influence of the Berezinskii–Kosterlitz–Thouless phase transition (BKT) that occurs at critical anisotropy point $$D_\mathrm{c}$$ , or the transition of the topological order of vortices and disordered phase on quantum entanglement.

Phases of translation-invariant systems out of equilibrium: iterative Green’s function techniques and renormalization group approaches

We introduce a method to evaluate the steady-state non-equilibrium Keldysh–Schwinger Green’s functions for infinite systems subject to both an electric field and a coupling to reservoirs. The method we present exploits a physical quasi-translation invariance, where a shift by one unit cell leaves the physics invariant if all electronic energies are simultaneously shifted by the magnitude of the electric field. Our framework is straightaway applicable to diagrammatic many-body methods. We discuss two flagship applications, mean-field theories as well as a sophisticated second-order functional renormalization group approach. The latter allows us to push the renormalization-group characterization of phase transitions for lattice fermions into the out-of-equilibrium realm. We exemplify this by studying a model of spinless fermions, which in equilibrium exhibits a Berezinskii–Kosterlitz–Thouless phase transition.