Yasuhiro Hatsugai

Chern numbers in discretized brillouin zone : Efficient method of computing (spin) hall conductances

We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb

We derive an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.We derive an efficient formula for Z

Entanglement entropy and the Berry phase in the solid state

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Quantum fluctuation of tunneling current in individual Ge quantum dots induced by a single-electron transfer

topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.

Topological aspects of the quantum spin-Hall effect in graphene: Z2 topological order and spin Chern number

The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one-dimensional (1D) cases, when the Berry phase (Zaks phase) of the occupied band is equal to

Quantized Berry Phases as a Local Order Parameter of a Quantum Liquid

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Exact analysis of entanglement in gapped quantum spin chains

and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than ln 2 (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss how this lower bound is related to vanishing of the expectation value of a certain nonlocal operator which creates a kink in 1D systems.

Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter

A scanning tunneling microscopic study revealed quantum fluctuation of tunneling currents in individual Ge quantum dots (QDs) on SiO2∕Si. This was due to the charging energy change in the QDs caused by single-electron transfer from or into the QDs. The observed electron discharging time of approximately milliseconds agreed with the propagation model of the electron wave packets from the QDs to the Si substrates by a tunneling effect rather than by passing through voids in the SiO2 smaller than electron de Broglie wavelength.

Characterization of Topological Insulators: Chern Numbers for Ground State Multiplet

For generic time-reversal-invariant systems with spin-orbit couplings, we clarify a close relationship between the

Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems

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