Related papers: Geometric Phase Transitions
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions…
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in…
We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via the…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using…
Geometric entanglement(GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. We outline a systematic method to compute GE for…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
Geometric phases have been extensively investigated in a wide range of quantum systems, often revealing deep connections to the underlying topology of many-body states. In this work, we examine two geometric phases defined for mixed quantum…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret…
While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the…
We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase…
The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate…
In a quantum measurement, a coupling $g$ between the system S and the apparatus A triggers the establishment of correlations, which provide statistical information about S. Robust registration requires A to be macroscopic, and a dynamical…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. Excluded volume effects are taken into account in the thermodynamically self-consistent way. The model exhibits a 1-st order phase…
The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model's phase structure and critical behavior in different…