Related papers: Generalized Hall Conductivities in Local Commuting…
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…
We consider the edge transport properties of a generic class of interacting quantum Hall systems on a cylinder, in the infinite volume and zero temperature limit. We prove that the large-scale behavior of the edge correlation functions is…
We discuss the topology of the parameter space of invertible phases with an onsite symmetry $G$, i.e., quantum many-body ground states that have neither fractionalization nor spontaneous breaking of the symmetry. The classification of…
We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The…
The Hall conductivity given by the Kubo formula is a linear response of the quantum transverse transport to a weak electric field. It has been intensively studied for a quantum system without decoherence, but it is barely explored for…
In QED of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be…
The Hall conductivity of disordered magnetic systems consisting of hard-core point vortices randomly dropped on the plane with a Poissonian distribution, has a behavior analogous to the one observed experimentally by R.~J.~Haug,…
We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract…
The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall…
By designing a multi-channel millimeter Hall measurement configuration, we realize the carrier-density (locally) controllable measurement on the transport property in 2H MoS$_{2}$. We observe a linearly increased Hall conductivity and…
We show that hybrid structures of topological insulators and materials without topological protection can be employed to create perfectly conducting channels hosted in the non-topological part. These states inherit the topological…
We investigate the interplay of generalized global symmetries in 2+1 dimensions in a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of…
We consider a generalization of the 2-dimensional (2D) quantum-Hall insulator to a non-compact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered 3D insulator with nontrivial…
We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The…
The checkerboard lattice is a two-dimensional non-trivial structure usually seen as a planar version of the pyrochlore lattice. This geometry supports a two-band insulating electronic system with Chern topology induced by a complex hopping…
We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and…
Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…
The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
The zero frequency conductivity ($D_c$), the criterion to distinguish between conductors and insulators is expressed in terms of a geometric phase. $D_c$ is also expressed using the formalism of the modern theory of polarization. The tenet…