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

The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…

The topological properties of the quantum Hall effect in a crystalline lattice, described by Chern numbers of the Hofstadter butterfly quantum phase diagram, are deduced by using a geometrical method to generate the structure of…

We study a family of pseudodifferential operators (quantum Hamiltonians) on $L^{2}(\mathbb{R}^{n};\mathbb{C}^{d})$ whose spectrum exhibits two energy bands exchanging a finite number of eigenvalues. We show that this number coincides with…

We study the spectra of quantum graphs with the method of trace identities (sum rules), which are used to derive inequalities of Lieb-Thirring, Payne-P\'olya-Weinberger, and Yang types, among others. We show that the sharp constants of…

Exact sum rules for the longitudinal and transverse part of the vector channel spectral functions at nonzero momentum are derived in the first part of the paper. The sum rules are formulated for the finite temperature spectral functions,…

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…

We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atom in optical lattices.…

Physical systems with non-trivial topological order find direct applications in metrology[1] and promise future applications in quantum computing[2,3]. The quantum Hall effect derives from transverse conductance, quantized to unprecedented…

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate…

Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains…

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…

Optical spectroscopy provides a powerful, contact-free probe of topological quantum states, yet exact constraints on antisymmetric Hall absorption remain much less well developed than their longitudinal counterparts. Motivated by earlier…

Topological materials are characterized by integer invariants that underpin their robust quantized electronic features, as famously exemplified by the Chern number in the integer quantum Hall effect. Yet, in most candidate systems, the…

In this series of lectures, we (re)view the "geometric method" that reconstructs, from a geometric object: the "spectral curve", an integrable system, and in particular its Tau function, Baker-Akhiezer functions and "current amplitudes",…

At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…

We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules…

We compare two widely used approaches to the description of hadron properties: QCD sum rules and constituent quark models. Making use of the dispersion formulation of the quark model, we show that both approaches lead to similar spectral…

4D CFTs have a scale anomaly characterized by the coefficient $c$, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point…

We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…