Kosterlitz-Thouless Research Articles

Perturbative study of the one-dimensional quantum clock model.

We calculate the ground-state energy density ε(g) for the one-dimensional N-state quantum clock model up to order 18, where g is the coupling and N=3,4,5,...,10,20. Using methods based on the Padé approximation, we extract the singular structure of ε^{″}(g) or ε(g). They correspond to the specific heat and free energy of the classical two-dimensional (2D) clock model. We find that, for N=3,4, there is a single critical point at g_{c}=1. The heat capacity exponent of the corresponding 2D classical model is α=0.34±0.01 for N=3, and α=-0.01±0.01 for N=4. For N>4, there are two exponential singularities related by g_{c1}=1/g_{c2}, and ε(g) behaves as Ae^{-c/|g_{c}-g|^{σ}}+analyticterms near g_{c}. The exponent σ gradually grows from 0.2 to 0.5 as N increases from 5 to 9, and it stabilizes at 0.5 when N>9. The phase transitions exhibited in these models should be generalizations of the Kosterlitz-Thouless transition, which has σ=0.5.

Cold-atom quantum simulator to explore pairing, condensation, and pseudogaps in extended Hubbard-Holstein models

We describe a quantum simulator for the Hubbard--Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing, and Berezinskii--Kosterlitz--Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed: (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon interactions and strong repulsion affects pairing in unconventional superconductors, (3) to understand the role of boson-mediated local pairing in pseudogaps and fermion condensates. We propose and study a quantum simulator for the HHM, using optical lattices, painted using zeros in the AC stark shift, to control two Rydberg atom species independently within a monolayer. We predict that interactions are sufficiently tunable to probe: (1) both HHMs and highly unconventional phonon-mediated repulsions, (2) the competition between intermediate-strength phonon and Coulomb mediated interactions, (3) BKT transitions, and preformed pairing that could be used to examine key hypotheses related to the pseudogap. We discuss how the quantum simulator can be used to investigate boson-mediated pairing and condensation of fermions in unconventional superconductors.

Many-body localization near the critical point

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $\textit{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \rightarrow \infty$, but the divergence is weaker than for the KT transition.

A New Method to Calculate a 2D Ising Universality Transition Point: Application near the Ashkin–Teller Multicritical Point

We propose a new method to numerically calculate transition points that belongs to 2D Ising universality class for quantum spin models. Generally, near the multicritical point, in conventional methods, a finite size correction becomes very large. To suppress the effect of the multicritical point, we use a z-axis twisted boundary condition and a y-axis twisted boundary condition. We apply our method to an S = 1/2 bond-alternating XXZ model. The multicritical point of this model has a BKT transition, where the correlation length diverges singularly. However, with our method, the convergence of calculation is highly improved, thus we can calculate the transition point even near the multicritical point.

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.

Vortex lattice in two-dimensional chiral XY ferromagnets and the inverse Berezinskii-Kosterlitz-Thouless transition

In this Letter we will show that, in the presence of a properly modulated Dzyaloshinskii-Moriya (DM) interaction, a $U(1)$ vortex-antivortex lattice appears at low temperatures for a wide range of the DM interaction. Even more, in the region dominated by the exchange interaction, a standard BKT transition occurs. In the opposite regime, the one dominated by the DM interaction, a kind of inverse BKT transition (iBKT) takes place. As temperature rises, the vortex-antivortex lattice starts melting by annihilation of pairs of vortex-antivortex, in a sort of "inverse" BKT transition.

The vortex state in FeSe superconducting thin film

We have investigated the low temperature isothermal current-voltage characteristics of FeSe epitaxial films with thickness of ∼ 360 nm at different magnetic fields parallel to the c axis. At zero magnetic field, with decreasing temperature a Berezinskii–Kosterlitz–Thouless transition, which often appears in two-dimensional (2D) superconductors, is observed. The current dependence of the voltage obeys the scaling relation V ∼ I 3 at the transition temperature K, and the temperature dependence of sheet resistance follows the prediction of the Halperin-Nelson formula in the vicinity of . When a magnetic field with magnitude 0.1 T T is applied, the low temperature isothermal current-voltage data in each field can be scaled onto two different branches by using the scaling relation predicted by the vortex-glass theory. When comparing with the scaling relation, the dimensionality D can only be taken as 2, indicating a vortex-liquid phase to quasi-2D vortex-glass phase transition occurs in the FeSe film. The presence of Berezinskii–Kosterlitz–Thouless transition and the quasi-2D vortex-glass phase are related to the weak coupling between Fe-Se layers in the FeSe film.

Ergodicity breaking transition in finite disordered spin chains

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. Using exact diagonalization we introduce a cost function approach to quantitatively compare different scenarios for the eigenstate transition. We study ergodicity indicators such as the eigenstate entanglement entropy and the spectral level spacing ratio, and we consistently find that an (infinite-order) Kosterlitz-Thouless transition yields a lower cost function when compared to a finite-order transition. Interestingly, we observe that the transition point in finite systems exhibits nearly thermal properties, i.e., ergodicity indicators at the transition are close to the random matrix theory predictions.

Two-dimensional superconductivity and magnetotransport from topological surface states in AuSn4 semimetal

Topological materials such as Dirac or Weyl semimetals are new states of matter characterized by symmetry-protected surface states responsible for exotic low-temperature magnetotransport properties. Here, transport measurements on AuSn4 single crystals, a topological nodal-line semimetal candidate, reveal the presence of two-dimensional superconductivity with a transition temperature Tc ~ 2.40 K. The two-dimensional nature of superconductivity is verified by a Berezinsky–Kosterlitz–Thouless transition, Bose-metal phase, and vortex dynamics interpreted in terms of thermally-assisted flux motion in two dimensions. The normal-state magnetoconductivity at low temperatures is found to be well described by the weak-antilocalization transport formula, which has been commonly observed in topological materials, strongly supporting the scenario that normal-state magnetotransport in AuSn4 is dominated by the surface electrons of topological Dirac-cone states. The entire results are summarized in a phase diagram in the temperature–magnetic field plane, which displays different regimes of transport. The combination of two-dimensional superconductivity and surface-driven magnetotransport suggests the topological nature of superconductivity in AuSn4.

Magnetic Field Induced Berezinskii-Kosterlitz-Thouless Correlations in 3-Dimensional Manganites

Ideal two-dimensional (2D) Heisenberg magnets lack long range magnetic order. However, the XY model with spins confined to a plane shows a topological phase transition at a finite temperature corresponding to binding and unbinding of vortices. Experimental evidence for such Berezinskii-Kosterlitz-Thouless (BKT) transitions has been difficult to obtain in condensed matter systems, where, even a weak interlayer coupling that is invariably present leads to long-range order, pre-empting the BKT transition. The BKT signatures are still discernible above the long-range ordering temperature, however, in the characteristic exponential temperature dependence of the coherence length of the fluctuations. In this work we report that an applied magnetic field can induce such BKT correlations not only in quasi 2-dimensional systems but also in nominally 3-dimensional manganites undergoing antiferromagnetic transitions. We arrive at this unexpected conclusion based on our studies of temperature dependence of electron paramagnetic resonance (EPR) linewidth ΔH(T) of Cr3+ doped bismuth strontium manganite Bi0.5Sr0.5Mn1-xCrxO3 (x= 0.04, 0.1) (BSMCO04 and BSMCO10).

Critical analysis of two-dimensional classical XY model

We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii–Kosterlitz–Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.

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.

Disordering a superfluid of light

A phase transition between disordered and quasi-ordered states, known as the Berezinskii–Kosterlitz–Thouless transition, has now been revealed in a two-dimensional photonic ‘fluid’. The interplay between phase singularities and coherence may lead to new vortex-based optical applications.

BKT transition of the XXZ ferromagnetic model on the spherical surface

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a well-known phenomenon on planar surfaces; however, for curved spaces, the situation is not clear. In this work, we applied the Self-consistent Harmonic Approximation (SCHA) to study the XXZ ferromagnetic model on the spherical surface. The Hamiltonian is written in terms of the canonically conjugate fields (operators in the quantum formalism) Sz and Φ that provide a renormalized spin stiffness depending on temperature. We consider both semiclassical and quantum approaches to the problem. The BKT transition is then determined by the temperature that provides abrupt vanishing of the spin stiffness. Our results show TBKT values close to that obtained for the planar model, and they are in agreement with the general aspects of the BKT phase transition theory.

Signatures of field-induced Berezinskii-Kosterlitz-Thouless correlations in the three-dimensional manganite Bi0.5Sr0.5Mn0.9Cr0.1O3

Despite experimental evidence for the two-dimensional topological Berezinskii-Kosterlitz-Thouless (BKT) transition in superconducting films and $^{4}\mathrm{He}$ superfluid films, the observation of a BKT transition in condensed matter systems has proven to be difficult. Potential signatures of BKT transitions were reported in two-dimensional magnets, however, the observation of a classical BKT transition in nominally three-dimensional systems has naturally not been investigated as the transition requires an underlying $XY$ model with spins confined to a plane. Here we report that the temperature dependence of the electron paramagnetic resonance (EPR) linewidth observed in ${\mathrm{Bi}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{O}}_{3}$ $(x=0.1 \mathrm{and} 0.04)$ as well as in certain other three-dimensional (3D) manganites undergoing antiferromagnetic transitions is described satisfactorily by the BKT model. We explain this unexpected observation of signatures of a two-dimensional topological phase transition in 3D systems in terms of an effective two-dimensional $XY$ easy plane anisotropy induced by the magnetic field applied in the EPR experiment that allows for the mediation of long-range vortex-like correlations between spin clusters formed due to phase segregation. This conclusion is supported by a re-analysis of EPR results reported earlier in La-doped ${\mathrm{CaMnO}}_{3}$ and a nonmanganite compound ${\mathrm{BaNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$. We infer that field-induced BKT correlations in a 3D system provide a step towards the observation of a BKT transition in a suitably chosen condensed matter system by the application of an appropriate magnetic field.

Topology of many-body edge and extended quantum states in an open spin chain: 1/3 plateau, Kosterlitz-Thouless transition, and Luttinger liquid

Quantum many-body edge and extended magnon excitations from the 1/3 -- plateau of the anisotropic Heisenberg model on an open AB$_2$ chain in a magnetic field $h$ are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and $h$ in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge states degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\lambda$ approaches the critical point from the $\lambda>0$ side of the phase diagram.

Dynamics of the Berezinskii–Kosterlitz–Thouless transition in a photon fluid

In addition to enhancing confinement, restricting optical systems to two dimensions gives rise to new photonic states, modified transport and distinct nonlinear effects. Here we explore these properties in combination and experimentally demonstrate a Berezinskii–Kosterlitz–Thouless phase transition in a nonlinear photonic lattice. In this topological transition, vortices are created in pairs and then unbind, changing the dynamics from that of a photonic fluid to that of a plasma-like gas of free (topological) charges. We explicitly measure the number and correlation properties of free vortices, for both repulsive and attractive interactions (the photonic equivalent of ferromagnetic and antiferromagnetic conditions), and confirm the traditional thermodynamics of the Berezinskii–Kosterlitz–Thouless transition. We also suggest a purely fluid interpretation, in which vortices are nucleated by inhomogeneous flow and driven by seeded instability. The results are fundamental to optical hydrodynamics and can impact two-dimensional photonic devices if temperature and interactions are not controlled properly. A topological transition in a nonlinear photonic lattice results in new vortex dynamics and a change from photonic fluid behaviour to that of a plasma-like gas.

The Berezinskii–Kosterlitz–Thouless Transition and Melting Scenarios of Two-Dimensional Systems

The paper discusses current theories of melting of two-dimensional systems that are mainly based on the concepts of the Berezinskii–Kosterlitz–Thouless (BKT) theory of phase transitions in two-dimensional systems with continuous symmetry. At present there are three basic scenarios of melting of two-dimensional crystals that as shown by computer simulation are implemented in the two-dimensional system of Hertzian spheres used to describe the behavior of a number of soft matter systems. The system demonstrates complex phase behavior with the presence of all three melting scenarios in the various parts of the phase diagram.

Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii–Kosterlitz–Thouless transition

In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and s-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii–Kosterlitz–Thouless (BKT) transition temperature TBKT to determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat-band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengths TBKT can be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model.

Spinless Fulde–Ferrell superfluid in Haldane model with nearest-neighbor interaction

Fulde–Ferrell (FF) state is an exotic superconducting or superfluid state, characterized by Cooper pairs with a finite center-of-mass momentum, and it has been intensively investigated in spinful systems, but the spin population imbalance is usually necessary. Here we propose a model to realize and modulate the spinless FF superfluid, namely, Haldane model with nearest-neighbor interaction. The FF state appears when the space-inversion and time-reversal symmetries are broken simultaneously, and there exists the first order phase transition. A higher Berezinskii–Kosterlitz–Thouless transition temperature is obtained at larger absolute value of Peierls phase and smaller energy offset of the sublattices. Our proposal provides a feasible option for experimental researchers to detect the FF superfluid.