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Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
We analyse a recently reported neutron interference experiment to measure a geometric phase and attempt to bring out the inadequacy of the ``phase modulo 2\pi" approach to the geometric phase. A modified neutron interferometer experiment to…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian…
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models,…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated to the topological order. The topology of these moduli spaces is used recently in the construction of Floquet codes. We…