Related papers: Large Scale Response of Gapless $1d$ and Quasi-$1d…
We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect…
We consider the dynamics of a class of weakly interacting, gapless $1d$ fermionic systems, in presence of small external perturbations slowly varying in space and in time. We consider the evolution of the expectation values of the charge…
We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d…
We demonstrate that the proper calculation of the linear response for finite-size systems can only be performed if the coupling to the leads/baths is explicitly taken into consideration. We exemplify this by obtaining a Kubo-type formula…
We consider Haldane-like $2d$ topological insulators on the cylinder, in the presence of weak quasi-periodic disorder. We prove that, at large distances, the boundary correlations agree with the correlations of a renormalized,…
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…
Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond…
We derive from first principles the Kubo formulas for the stress-stress response function at zero wavevector that can be used to define the full complex frequency-dependent viscosity tensor, both with and without a uniform magnetic field.…
We investigate spin transport in 2-dimensional insulators, with the long-term goal of establishing whether any of the transport coefficients corresponds to the Fu-Kane-Mele index which characterizes 2d time-reversal-symmetric topological…
We consider a class of two-dimensional tight binding models displaying conical intersections of the Bloch bands at the Fermi level. The setting includes the case of generic transitions between quantum Hall phases. We consider the…
In this article we study the thermal response functions for two one-dimensional models, namely the Hubbard and spin-less fermion $t$-$V$ models. By exactly diagonalizing finite sized systems we calculate dynamical electrical,…
The traditional Kubo formula is generalized to describe the linear response with respect to non-Abelian fields. To fulfil the demand for studying spin transport, the SU(2) Kubo formulae are derived by two conventional approaches with…
We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A…
We consider an ergodic Schr\"odinger operator with magnetic field within the non-interacting particle approximation. Justifying the linear response theory, a rigorous derivation of a Kubo formula for the electric conductivity tensor within…
The quantized thermal Hall effect is an important probe for detecting chiral topological order and revealing the nature of chiral gapless edge states. The standard Kubo formula approach for the thermal Hall conductance $\kappa_{xy}$ based…
Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight…
We explore the robustness of Hall conductivity quantization in several insulating systems, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the…
We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is…
The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. \cite{BELLISSARD:1994xj,Schulz-Baldes:1998vm,Schulz-Baldes:1998oq}. This formula was derived…
Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a…