Abstract:
The quantum XY model shows a Berezinskii-Kosterlitz-Thouless (BKT) transition between a phase with quasi long-range order and a disordered one, like the corresponding classical model. The effect of the quantum fluctuations is to weaken the transition and eventually to destroy it. However, in this respect the mechanism of disappearance of the transition is not yet clear. In this work we address the problem of the quenching of the BKT in the quantum XY model in the region of small temperature and high quantum coupling. In particular, we study the phase diagram of a 2D Josephson junction array, that is one of the best experimental realizations of a quantum XY model. A genuine BKT transition is found up to a threshold value $g^\star$ of the quantum coupling, beyond which no phase coherence is established. Slightly below $g^\star$ the phase stiffness shows a reentrant behavior at lowest temperatures, driven by strong nonlinear quantum fluctuations. Such a reentrance is removed if the dissipation effect of shunt resistors is included.

Abstract:
The 2d XY model exhibits an essential phase transition, which was predicted long ago --- by Berezinskii, Kosterlitz and Thouless (BKT) --- to be driven by the (un)binding of vortex--anti-vortex pairs. This transition has been confirmed for the standard lattice action, and for actions with distinct couplings, in agreement with universality. Here we study a highly unconventional formulation of this model, which belongs to the class of topological lattice actions: it does not have any couplings at all, but just a constraint for the relative angles between nearest neighbour spins. By means of dynamical boundary conditions we measure the helicity modulus Upsilon, which shows that this formulation performs a BKT phase transition as well. Its finite size effects are amazingly mild, in contrast to other lattice actions. This provides one of the most precise numerical confirmations ever of a BKT transition in this model. On the other hand, up to the lattice sizes that we explored, there are deviations from the spin wave approximation, for instance for the Binder cumulant U_4 and for the leading finite size correction to Upsilon. Finally we observe that the (un)binding mechanism follows the usual pattern, although free vortices do not require any energy in this formulation. Due to that observation, one should reconsider an aspect of the established picture, which estimates the critical temperature based on this energy requirement.

Abstract:
We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tuneable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation (BEC) transition in the limit of vanishing interactions.

Abstract:
We study the flux noise in Josephson junction arrays in the critical regime above the Berezinskii-Kosterlitz-Thouless transition. In proximity coupled arrays a local ohmic damping for the phases is relevant, giving rise to anomalous vortex diffusion and a dynamic scaling of the flux noise in the critical region. It shows a crossover from white to $1/f$-noise at a frequency $\omega_\xi\propto\xi^{-z}$ with a dynamic exponent $z=2$.

Abstract:
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.

Abstract:
The Berezinskii-Kosterlitz-Thouless theory for superfluid films is generalized in a straightforward way that (a) corrects for overlapping vortex-antivortex pairs at high pair density and (b) utilizes a dielectric approximation for the polarization of the vortex system and a local field correction. Generalized Kosterlitz equations are derived, containing higher order terms, which are compared with earlier predictions. These terms cause the total pair density to remain finite for temperatures above the transition so that it is not necessary to introduce an ad hoc cut-off, as opposed to the original Berezinskii-Kosterlitz-Thouless theory. The low-temperature bound pair phase is destabilized for small vortex core energy. The behaviour of the stiffness constant and of the correlation length close to the transition is not affected by the higher order terms. A first-order transition as suggested by other authors is not found for any values of the parameters. The pair density is calculated for temperatures below and above the transition. Possible experiments and the applicability of the extended approach are discussed. The approach is found to be applicable even in a significant temperature range above the transition.

Abstract:
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an attempt to fully understand the nature of its transition, which is of the Berezinskii-Kosterlitz-Thouless type. These met with only limited success until it was realized that subtle effects (logarithmic corrections) that modify leading behaviour must be taken into account. This realization prompted renewed activity in the field and significant progress has been made. This paper contains a review of the importance of such subtleties, the role played by vortices and of recent and current research in this area. Directions for desirable future research endeavours are outlined.

Abstract:
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 point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface.

Abstract:
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 construct holographic renormalization for probe branes in the ABJM theory and propose a scheme for the little string theory. Finally, we obtain the embeddings and (half of) the meson spectrum in the ABJM theory with massive flavor.

Abstract:
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 $\chi_c- \chi(\lambda)\sim \sqrt{|\lambda_c-\lambda|} $, where $\lambda$ is a parameter driving the transition, and $\chi_c$ is the peak value at the transition point $\lambda=\lambda_c$. Numerical claims of the logarithmic divergence of fidelity susceptibility with the system size (or temperature) are explained by logarithmic corrections due to marginal operators, which is supported by numerical calculations for large systems.