Hall conductivity as a topological invariant

The object of the present work is to study the quantum Hall effect through its symmetries and topological aspects. We consider the model of an electron moving in a two-dimensional lattice in the presence of applied in-plain electric field and perpendicular magnetic field. We refer to this as the two dimensional electric-magnetic Bloch problem (EMB). The Hall conductivity quatizations beyond the linear response approximation is analyzed.Comment: 6 page

Quantum simulation of the von Neumann equation of time-dependent Hamiltonians

In this work we develop a quantum algorithm to simulate the dynamics of the density matrix governed by the von Neumann equation for time-dependent Hamiltoinans. The method relies on the vectorization of the density matrix through the properties of the structure constants of a given Lie algebra. Even though we have used the algebra formed by the Pauli strings, the algorithm can be easily adapted to other algebras. One of the main advantages of this approach is that it yields real density matrix coefficients that are easy to determine through phase kickback. The algorithm is demonstrated using the IBM noisy quantum circuit simulator.Comment: 8 pages, 7 figure

Symmetry breaking as the origin of zero-differential resistance states of a 2DEG in strong magnetic fields

Zero resistance differential states have been observed in two-dimensional electron gases (2DEG) subject to a magnetic field and a strong dc current. In a recent work we presented a model to describe the nonlinear transport regime of this phenomenon. From the analysis of the differential resistivity and the longitudinal voltage we predicted the formation of negative differential resistivity states, although these states are known to be unstable. Based on our model, we derive an analytical approximated expression for the Voltage-Current characteristics, that captures the main elements of the problem. The result allow us to construct an energy functional for the system. In the zero temperature limit, the system presents a quantum phase transition, with the control parameter given by the magnetic field. It is noted that above a threshold value ($B>B_{th}$), the symmetry is spontaneously broken. At sufficiently high magnetic field and low temperature the model predicts a phase with a non-vanishing permanent current; this is a novel phase that has not been observed so far.Comment: 6 pages, 2 figure