Related papers: Information Geometry and Quantum Phase Transitions…
We explore the influence of geometry in the critical behavior of sparse long-range spin models. We examine a model with interactions that can be continuously tuned to induce distinct changes in the metric, topology, and dimensionality of…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
We study the thermodynamics and thermodynamic geometry of a five-dimensional Reissner-Nordstr\"om-AdS black hole in the extended phase space by treating the cosmological constant as being related to the number of colors in the boundary…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…
The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode. We point out that in the strong…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
We perform a statistical and geometrothermodynamic analysis of three different models of magnetic materials, namely, the translational free model, the spin model, and the mean-field model. First, we derive the fundamental equation for each…
We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex…
In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed…
The dimerized Kane-Mele model with/without the strong interaction is studied using analytical methods. The boundary of the topological phase transition of the model without strong interaction is obtained. Our results show that the…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The single-mode Dicke model is well-known to undergo a quantum phase transition from the so-called normal phase to the supperradiant phase (hereinafter called the "superradiant quantum phase transition"). Normally, quantum phase transitions…
We consider the possibility of quantum phase transitions in the ground state of triplet superconductors where particle density is the tunning parameter. For definiteness, we focus on the case of one band quasi-one-dimensional triplet…
We study magnetic materials whose low energy physics can be effectively described by a Dicke model, which we term Dicke materials. We show how a Dicke model emerges in such materials due to a coexistence of fast-dispersing and…
In this paper, we examine the thermodynamic geometry of four-dimensional quasi-topological black holes by computing the Ruppeiner scalar curvature R which serves as an empirical tool to describe the nature of interactions among black hole…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…