Chebyshev expansion for Impurity Models using Matrix Product States

We improve a recently developed expansion technique for calculating real frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can be achieved at virtually no cost and, in sharp contrast to existing methods based on the dampening of the moments, improves the spectral resolution rather than lowering it. We validate the method for the exactly solvable resonating level model and the single impurity Anderson model. It is capable of resolving sharp Kondo resonances, as well as peaks within the Hubbard bands when employed as an impurity solver for dynamical mean-field theory (DMFT). Our method works at zero temperature and allows for arbitrary discretization of the bath spectrum. It achieves similar precision as the dynamical density matrix renormalization group (DDMRG), at lower cost. We also propose an alternative expansion, of 1-exp(-tau H) instead of the usual H, which opens the possibility of using established methods for the time evolution of matrix product states to calculate spectral functions directly.Comment: 13 pages, 9 figure

Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at $k = 0$ and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments