Related papers: A Comment On Berry Connections
The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological…
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We…
We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the…
In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian…
Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization is hindered by an intrinsic ambiguity rooted in the eigenspace of non-Hermitian Hamiltonians, which…
Berry phase was originally defined for systems whose states are separated by finite energy gaps. One might naively expect that a system without a gap cannot have a Berry phase. Despite this we ask whether a Berry phase can be observed in a…
Berry connection has been recently generalized to higher-dimensional QFT, where it can be thought of as a topological term in the effective action for background couplings. Via the inflow, this term corresponds to the boundary anomaly in…
The Berry connection describes transformations induced by adiabatically varying Hamiltonians. We study how zero modes of the modular Hamiltonian are affected by varying the region that supplies the modular Hamiltonian. In the vacuum of a 2d…
We study the connection between Berry phases and quantum phase transitions of generic quantum many-body systems. Consider sequences of Berry phases associated to sequences of loops in the parameter space whose limit is a point. If the…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons…
It has been recently found that the equations of motion of several semiclassical systems must take into account anomalous velocity terms arising from Berry phase contributions. Those terms are for instance responsible for the spin Hall…
The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure…
The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to…
In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this…
We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there…
Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
Laplacians on metric graphs are used to construct continuous families of Hamiltonians with different topological structure. One such family is used to demonstrate that Hamiltonians with real-valued eigenfunctions may possess non-trivial…