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Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the…
We establish an exact analytical relation between Zitterbewegung dynamics and the band geometry in two-dimensional Dirac systems. By identifying a time-independent antisymmetric observable-the \textit{areal rate of Zitterbewegung}-we show…
The diagonal nonadiabatic term arising from the Born--Oppenheimer wave-function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the…
We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term…
We investigate chiral superconductivity emerging from parent electronic states with non-uniform Berry curvature, motivated by recent experiments in rhombohedral graphene multilayers. Using the continuum $\lambda_N$-model-a tunable platform…
Stimulated by the recent realization of three dimensional topological insulator nanowire interfer- ometers, a theoretical analysis of quantum interference effects on the low energy spectrum of Bi2Se3 nanowires is presented. The electronic…
Flat-band superconductors provide a regime in which kinetic energy is quenched, so that pairing is governed primarily by interactions and quantum geometry. We investigate characteristic superconducting length scales in all-flat-band systems…
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting…
The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are…
As reflection symmetry or space-time inversion symmetry is preserved, with a non-contractible integral loop respecting the symmetry in the Brilliouin zone, Berry phase is quantized in proper basis. Topological nodal lines can be enclosed in…
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…
The Berry curvature (BC) - a quantity encoding the geometric properties of the electronic wavefunctions in a solid - is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst…
The new superconductivity theory that attributes the $U(1)$ superconductivity phase to a Berry phase arising from many-body wave functions is applied to the circuit quantization for superconducting qubits. The phase-charge duality required…
We study infrared divergences in quantum electrodynamics using geometric phases and the adiabatic approximation in quantum field theory. In this framework, the asymptotic \textit{in} and \textit{out} states are modified by Berry phases,…
We analytically investigate the non-equilibrium pumping for a double quantum dots system on the basis of the quantum master equation (QME), where the double quantum dots are connected to two external leads by the spin coupling. Each of…
One milestone in quantum physics is Berry's seminal work [Proc.~R.~Soc.~Lond.~A \textbf{392}, 45 (1984)], in which a quantal phase factor known as geometric phase was discovered to solely depend on the evolution path in state space. Here,…
The exploration of the Berry phase in classical mechanics has opened new frontiers in understanding the dynamics of physical systems, analogous to quantum mechanics. Here, we show controlled accumulation of the Berry phase in a two-level…
We investigate the quantum geometric tensor, which is comprised of the Berry curvature and quantum metric, in a generalized Dirac two-band system with non-integer dispersion $E(\mathbf{k})\sim k^{\alpha}$. Our analysis reveals that this…
The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state…
This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian,…