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The property of XY model with its KT phase transition has been discussed in many aspects such as specific heat and magnetic susceptibility along with correlation function. Also, this is one of the original models for topological phase transition which gives a new type of phase transition without symmetry breaking. Since the calculation of these properties above can be achieved by Monte Carlo Method with Wolff algorithm, the visualization of vortex and antivortex is also an interesting task which is accomplished in this article. By successfully modeling the system and getting the step-by-step configuration, the relation between the generation of vortex and the variation of temperature can be concluded in a qualitative way. The calculation of spin correlation function shows the phase transition between disorder and quasi long-range order which represents the topological phase transition. As a reliable method, the Monte Carlo method with Wolff algorithm can be a choice of generating the training set for neural network which can calculated much more sophisticated case in a relatively short time and the transition between classical simulation and quantum simulation can be approached as mentioned in the end of this article.

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) T -matrix approximation (TMA). In the two-dimensional case, while this strong-coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improves TMA to include higher-order pairing fluctuations within the framework of a self-consistent T -matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional 6 Li Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order.

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a T -matrix approximation, we calculate the distribution function n ( Q ) of Cooper pairs in terms of the center of mass momentum Q . In the strong-coupling regime, n ( Q = 0 ) is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional 6 Li Fermi gas (Ries et al. in Phys Rev Lett 114:230401, 2015 ). Our result indicates that the observed remarkable increase of the number of Cooper pairs with zero center of mass momentum can be explained without assuming the Berezinskii–Kosterlitz–Thouless (BKT) transition, when one properly includes pairing fluctuations that are enhanced by the low-dimensionality of the system. Since the BKT transition is a crucial topic in two-dimensional Fermi systems, our results would be useful for the study toward the realization of this quasi-long-range order in an ultracold Fermi gas.

Many two-dimensional physical systems ranging from atomic-molecular condensates to low-dimensional superconductors and liquid-crystal films are described by coupled XY models. The interplay of topology and competing interactions in these XY systems drives new kinds of emergent behavior relevant in both quantum and classical settings. Such coupled U(1) systems further introduce rich physics, bringing topology into contact with fractionalization and deconfinement. Motivated by a hidden-order phase transition in isotropic liquid-crystal 54COOBC films, we study the finite-temperature phase diagram of a minimalist hexatic-nematic XY model. We identify a small region of composite Potts order above the vortex-binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. We propose that the Potts order results from a confinement of fractional vortices into extended nematic defects and discuss the broader implications of fractional vortices and composite ordering in the wider class of coupled XY condensates.

We have studied how substitutions of magnetic Ni and nonmagnetic Zn in copper sites of Y 3 Ba 5 Cu 8 O 18– δ  (Y-358) affect critical temperature and the nonlinear behavior of current–voltage ( IV ) characteristics in the zero magnetic field. An exponent as a function of temperature ( T ) has been extracted to understand nonlinearity of IV within the framework of the BKT transition. We have extracted superfluid phase stiffness as a function of T of both groups of samples using the nonlinear exponent and the Ambegaokar–Halperin–Nelson–Siggia (AHNS) theory. The linear nature of the suppression of the critical temperature by Zn is found to be stronger than that of Ni. A strong suppression of the superfluid phase stiffness (SPS) by both dopants has also been observed. However, the suppression of the SPS with T by the nonmagnetic Zn is entirely different in comparison with the nonlinear suppression by the magnetic Ni.

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

Superconducting nanofilms are tunable systems that can host a 3D–2D dimensional crossover leading to the Berezinskii–Kosterlitz–Thouless (BKT) superconducting transition approaching the 2D regime. Reducing the dimensionality further, from 2D to quasi-1D superconducting nanostructures with disorder, can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase-fluctuation phenomena of difficult experiments. We characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature-dependent resistivity and current–voltage (I-V) characteristics. Our measurements evidence clear features related to the emergence of BKT transition and PS events. The contemporary observation in the same system of BKT transition and PS events, and their tunable evolution in temperature and thickness was explained as due to the nano-conducting paths forming in a granular NbN system. In one of the investigated samples, we were able to trace and characterize the continuous evolution in temperature from quantum to thermal PS. Our analysis established that the detected complex phase phenomena are strongly related to the interplay between the typical size of the nano-conductive paths and the superconducting coherence length.

The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition in quasi-two-dimensional superconductors still remains a controversial issue. Its main signatures, indeed, are often at odds with the theoretical expectations. In a recent work (Maccari, I.; Benfatto, L.; Castellani, C. Phys. Rev. B 2017, 96, 060508), we have shown that the presence of spatially correlated disorder plays a key role in this sense because it is the reason underlying the experimentally-observed smearing of the universal superfluid-density jump. In the present paper we closely investigate the effects of correlated disorder on the BKT transition, specifically addressing the issue of whether or not it changes the BKT universality class.

Based on an attractive U Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we finally arrive at is of the extended XY type. While it correctly reduces to a simple XY in the continuum limit, in the general case, it contains higher neighbor interaction in spin space. An important feature of our Hamiltonian is that it gives a much larger fluctuation region between the Berezinskii–Kosterlitz–Thouless transition temperature identified with Tc for superconducting and the mean field transition temperature identified with the pseudogap temperature.