相关论文: Topological properties of geometric phases
The level crossing problem and associated geometric terms are neatly formulated by the second quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete…
By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a…
The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one…
The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and the lines bundle L^n over M such that the adiabatic geometric phases associated with the…
The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of…
We study a one-dimensional interacting topological model by means of exact diagonalization method. The topological properties are firstly examined with the existence of the edge states at half-filling. We find that the topological phases…
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls…
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
Time does not obviously appear amongst the coordinates on the constrained phase space of general relativity in the Hamiltonian formulation. Recent work in finite-dimensional models claims that topological obstructions generically make the…
Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…