相关论文: Spectral sum rules reflect topological and quantum…

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations…

We study homogenisation problems for divergence form equations with rapidly sign-changing coefficients. With a focus on problems with piecewise constant, scalar coefficients in a ($d$-dimensional) crosswalk type shape, we will provide a…

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…

A topological superconductor is a fully gapped superconductor that exhibits exotic zero-energy Andreev surface states at interfaces with a normal metal. In this paper we investigate the properties of a three-dimensional time reversal…

We derive spectral sum rules for inverse powers of the eigenvalues of the Helmholtz equation on a $d$-sphere in the presence of an arbitrary density. By adopting a rigorous renormalization scheme, we remove the divergent contributions of…

In the absence of any symmetry constraints we address universal properties of the boundary charge $Q_B$ for a wide class of nearest-neighbor tight-binding models in one dimension with one orbital per site but generic modulations of on-site…

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The…

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…

In theory of topological classification, the 2D topological superconductors without time reversal symmetry are characterized by Chern numbers. However, in reality, we find the Chern numbers can not reveal the whole properties of the…

We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including N\'eel antiferromagnetic…

Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain…

We propose a geometric criterion of the topological phase transition for non-Hermitian systems. We define the length of the boundary of the bulk band in the complex energy plane for non-Hermitian systems. For one-dimensional systems, we…

We show that the leading double spectral density in sum rules for Compton-like processes can be obtained by simple properties of the Borel transform, extending an approach widely used in the literature on sum rules, and known to be valid…

Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation…

Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…

We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…

Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…

Using semi-classical analysis in $\mathbb{R}^{n}$ we present a quite general model for which the topological index formula of Atiyah-Singer predicts a spectral flow with the transition of a finite number of eigenvalues between clusters…

The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…