In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigen-equation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A new hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meets at a multi-critical point, from which a deconfinement crossover line extends into the disordered phase.
We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane, and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattice…
Occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition is investigated by superfluid density measurements for two-dimensional (2D) disordered NbN films with disorder level very close to a superconductor-insulator transition (SIT). Our data show a robust BKT transition even near this 2D disorder-tuned quantum critical point (QCP). This observation is in direct contrast with previous data on deeply underdoped quasi-2D cuprates near the SIT. As our NbN films approach the QCP, the vortex-core energy, an important energy scale in the BKT transition, scales with the superconducting gap, …
We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the mul…
We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. Furthermore, we study the influence of a nearby magnetic quantum critical poi…
Assuming that two-component Fermi gases with opposite artificial magnetic fields on a square optical lattice are well-described by the so-called time-reversal-symmetric Hofstadter-Hubbard model, we explore the thermal superfluid properties along with the critical Berezinskii-Kosterlitz-Thouless (BKT) transition temperature in this model over a wide-range of its parameters. In particular, since our self-consistent BCS-BKT approach takes the multi-band butterfly spectrum explicitly into account, it unveils how dramatically the inter-band contribution to the phase stiffness dominates the intra-ba…
We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension c…
The spin relaxation in chromium spinel oxides $A$Cr$_{2}$O$_{4}$ ($A=$ Mg, Zn, Cd) is investigated in the paramagnetic regime by electron spin resonance (ESR). The temperature dependence of the ESR linewidth indicates an unconventional spin-relaxation behavior, similar to spin-spin relaxation in the two-dimensional (2D) chromium-oxide triangular lattice antiferromagnets. The data can be described in terms of a generalized Berezinskii-Kosterlitz-Thouless (BKT) type scenario for 2D systems with additional internal symmetries. Based on the characteristic exponents obtained from the evaluation of …
We find the first example of a quantum Berenzinskii-Kosterlitz-Thouless (BKT) phase transition in two spatial dimensions via holography. This transition occurs in the D3/D5 system at nonzero density and magnetic field. At any nonzero temperature, the BKT scaling is destroyed and the transition becomes second order with mean-field exponents. We go on to conjecture about the generality of quantum BKT transitions in two spatial dimensions.
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.
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 …
An attempt is made to find different emergent quantum phases for interacting topological state of quantum matter. Our study is based on the quantum field theoretical renormalization group (RG) calculations. The behaviour of the RG flow lines gives the emergence of different quantum phases for non-interacting and interacting topological state of quantum matter. We show explicitly electron-electron interaction can turn a topologically trivial phase into a non-trivial one and also topological non-trivial phase to topological trivial phase. We show that physics of emergent is go beyond the quantum…
Motivated by recent experimental progress in 2D magnetism, we theoretically study spin transport in 2D easy-plane magnets at finite temperatures across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, by developing a duality mapping to the 2+1D electromagnetism with the full account of spin's finite lifetime. In particular, we find that the non-conservation of spin gives rise to a distinct signature across the BKT transition, with the spin current decaying with distance power-law (exponentially) below (above) the transition; this is detectable in the proposed experiment with NiPS$_3…
Proliferation of defects is a mechanism that allows for topological phase transitions. Such a phase transition is found in two dimensions for the XY-model, which lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. The transition point can be found using renormalization group analysis. We apply renormalization group arguments to determine the nature of BKT transitions for the three-dimensional plaquette-dimer model, which is a model that exhibits fractonic mobility constraints. We show that an important part of this analysis demands a modified dimensional analysis that changes…
In the two-dimensional superfluidity, the proliferation of the vortices and the anti-vortices results in a new class of phase transition, Berezinskii-Kosterlitz-Thouless (BKT) transition. This class of the phase transitions is also anticipated in the two-dimensional magnetic systems. However, its existence in the real magnetic systems still remains mysterious. Here we propose a phenomenological model to illustrate that the novel spin-freezing transition recently uncovered in the NMR experiment on the NiGa_2S_4 compound is the BKT-type. The novel spin-freezing state observed in the NiGa_2S_4 po…
We find that the temperature dependence of the Electron Paramagnetic Resonance (EPR) linewidth observed in Bi$_{0.5}$Sr$_{0.5}$Mn$_{0.9}$Cr$_{0.1}$O$_3$ (BSMCO), as well as in certain other 3-dimensional manganites undergoing antiferromagnetic transitions is satisfactorily described by the Berezinskii-Kosterlitz-Thouless (BKT) model. We understand this unexpected result in terms of an effective 2-dimensional XY easy plane anisotropy induced by the magnetic field applied in the EPR experiment. This conclusion is supported by the field dependence of the BKT correlations observed in the quasi two…
We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction based on the Gaussian approximation of the Luttinger liquid approach, it is shown that the fidelity susceptibility does not diverge at the transition, but has a cusp-like peak $χ_c- χ(λ)\sim \sqrt{|λ_c-λ|} $, where $λ$ is a parameter driving the transition, and $χ_c$ is the peak value at the transition point $λ=λ_c$. Numerical claims of the logarithmic diverg…
This is a set of notes recalling some of the most important results on the XY model from the ground up. They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D classical XY model. The connection to the 2D Coulomb gas is presented in detail, as well as the renormalization group flow obtained from this dual representation. A numerical Monte-Carlo approach to the classical XY model is presented. Finally, two physical setting that realize the celebrated Kosterlitz-Thouless phase transition are presented: superfluid and l…
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 litera…
We discuss the d=2 quantum O(2)xO(2) nonlinear sigma model as a low-energy theory of phase reconstruction near a quantum critical point. We first examine the evolution of the Berezinskii-Kosterlitz-Thouless (BKT) transition as the quantum limit is approached in the usual O(2) nonlinear sigma model. Then we go on to review results on the ground-state phase diagram of the O(2)xO(2) nonlinear sigma model, and on the behaviour of the O(2)xO(M) nonlinear sigma model with M>2 in the classical limit. Finally, we present a conjectured finite-temperature phase diagram for the quantum version of the lat…
We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at $J_c$ to $J^*$ in the gapped phase by a value $|J^* - J_c| = B^2/36$, where $B^2$ is a transition width controlling the asymptotic form of the correlation length $ξ\sim \exp(-B/\sqrt{|J-J_c|})$ in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity …
We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime ar…
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are s…
We find two systems via holography that exhibit quantum Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. The first is the ABJM theory with flavor and the second is a flavored (1,1) little string theory. In each case the transition occurs at nonzero density and magnetic field. The BKT transition in the little string theory is the first example of a quantum BKT transition in (3+1) dimensions. As in the "original" holographic BKT transition in the D3/D5 system, the exponential scaling is destroyed at any nonzero temperature and the transition becomes second order. Along the way we constru…
We present the ground state wave functions for systems of one-dimensional interacting fermions. It is shown that these systems undergo phase transitions similar to the Kosterlitz-Thouless one independently of the interaction details. In the limit of an infinitely strong interaction the phase transition turns into the usual second order phase transition in a chiral phase. The temperature of the phase transition is calculated.
We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wavefunctions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact…
We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte-Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures…
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO$_4$, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. M…
We have made a detailed study of the phase structure for lattice Schwinger model with one flavor of Wilson fermion on the $(m,g)$ plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The B…
Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenolog…
We employ a novel, unbiased renormalization-group approach to investigate non-equilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low dimensions out of equilibrium. We study a prototypical model for the metal to insulator transition of spinless interacting fermions coupled to electronic baths and driven out of equilibrium by a longitudinal static electric field. The closed system features a Berezinskii-Kosterlitz-Thouless transition between a metallic and a charge-ordered phase in the equilibrium …
We study the superconducting Kosterlitz-Thouless transition of the attractive Hubbard model on a two-dimensional triangular lattice using auxiliary field quantum Monte Carlo method for system sizes up to $12\times 12$ sites. Combining three methods to analyze the numerical data, we find, for the attractive interaction of $U=-4t$, that the transition temperature stays almost constant within the band filling range of $1.0 < n < 1.4$, while it is found to be much lower in the $n<1$ region.
We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interacti…
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 $β=d\ln g/d\ln M$ indicates that the metal-insulator transition is Kosterlitz-Thouless (KT) type, which is characterized by bounding and unbounding of vortex-antivortex pairs of the local currents. The KT like metal-insulator transition is a basic characteristic of the quantum s…
