Related papers: Geometric quenches in quantum integrable systems
We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A…
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…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
We consider a problem of geometric phase generation in a system of two interacting bosons confined in a narrow ring potential with a localized defect. Geometric phase emerges from variation of parameters of the defect. Particle interaction…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
We investigate an integrable boundary quench, in which one integrable boundary condition is suddenly switched to another. We develop a general framework for analyzing the resulting real-time dynamics based on form factors of bulk and…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
In this paper we introduce a geometric framework for mixed quantum states based on a K\"ahler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics,…
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…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent many-body system, it can occur in an…
We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the…
A quantum many-body system undergoes phase transitions of distinct species with variations of local and global parameters. We propose a framework in which a dynamical quantity can change its behavior for quenches across global…
We study the off-equilibrium dynamics of the infinite dimensional Bose Hubbard Model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical…
We study many-body quantum geometric effects in time-dependent system with emergent quantum integrable field theory instantaneously. We establish a theorem stating that the Berry connection matrix thus all associated geometric quantities of…
Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models…
An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state…