Related papers: Berry phase and quantum structure
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
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 phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…
The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…
We show that quantum interference can be classically interpreted in terms of a phase invariant quantity, not unlike the Berry's phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Recent numerical simulations of flat band models with interactions which show clear evidence of fractionalized topological phases in the absence of a net magnetic field have generated a great deal of interest. We provide an explanation for…
By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We develop a semiclassical theory for the dynamics of electrons in a magnetic Bloch band, where the Berry phase plays an important role. This theory, together with the Boltzmann equation, provides a framework for studying transport problems…
The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
For decades, ``geometry" in band theory has largely meant Berry phase and Berry curvature-quantities that reshape semiclassical dynamics and underpin modern topological matter. Yet the full geometric content of a Bloch band is richer and…
Analytical calculations and micromagnetic simulations are used to determine the Berry curvature and topological Hall effect (THE) due to conduction electrons in small ferromagnetic particles. Our focus is on small particles of…
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…
Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection…
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution…