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Phase transitions give crucial insight into many-body systems, as crossovers between different regimes of order are determined by the underlying dynamics. These dynamics, in turn, are often constrained by dimensionality and geometry. For…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
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 large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at…
We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed…
The Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behaviour of a wide range of equilibrium two-dimensional systems with a continuous…
B-T phase diagram and phase transitions of interlayer Josephson vortices are investigated. For magnetic fields above a critical value, we find a Kosterlitz-Thouless (KT) type intermediate phase characterized by in-plane two-dimensional,…
The classical XY model has been consistently studied since it was introduced more than six decades ago. Of particular interest has been the two-dimensional spin model's exhibition of the Berezinskii-Kosterlitz-Thouless (BKT) transition.…
XY models with continuous spin orientation play a pivotal role in understanding topological phase transitions and emergent frustration phenomena, such as superconducting and superfluid phase transitions. However, the complex energy…
We perform quantum Monte Carlo simulations to study the 2D hard-core Bose-Hubbard model in a random potential. Our motivation is to investigate the effects of randomness on the Kosterlitz--Thouless (KT) transition. The chemical potential is…
Any state of matter is classified according to its order, and the kind of order a physical system can posses is profoundly affected by its dimensionality. Conventional long-range order, like in a ferromagnet or a crystal, is common in…
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,…
In layered superconductors with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless (KT) behavior are expected to be observable at some energy scale…
Efficient and automated classification of phases from minimally processed data is one goal of machine learning in condensed matter and statistical physics. Supervised algorithms trained on raw samples of microstates can successfully detect…
It has been known that encoding Boltzmann weights of a classical spin model in amplitudes of a many-body wave function can provide quantum models whose phase structure is characterized by using classical phase transitions. In particular,…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models these are vortices: above a…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a typical topological phase transition defined between binding and unbinding states of vortices and antivortices, which is not accompanied by spontaneous symmetry breaking. It is known…
Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with $C_3$ symmetry breaking upon an…
In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo…
The experimental investigation of spontaneously created vortices is of utmost importance for the understanding of quantum phase transitions towards a superfluid phase, especially for two dimensional systems that are expected to be governed…