Spectral Statistics of Many-Body Systems by the Duality Approach

Mathematical Physics Seminar

November 15, 2018 @ 14:00

Dr. Boris Gutkin (H.I.T.) will give a talk on "Spectral Statistics of Many-Body Systems by the Duality Approach".

Abstract

The Hilbert space dimension of many-body quantum Hamiltonians grows exponentially fast with the number of system constituencies hindering a direct numerical or analytical evaluation of their spectra. I will show how this problem can be circumvented for chain like systems with local interactions, provided one is interested in long range spectral statistics. Our approach is based on the duality relation which connects traces of the unitary evolution in time to those of a dual, non-unitary evolution in space. In contrast to the time evolution, the dimension of the corresponding dual operator is independent of the system size. Furthermore, for short time propagation this dimension remains relatively small making numerical and analytic approaches to long-range spectral statistics feasible. I will present a few concrete applications of the method.

Place: Holon Institute of Technology, Faculty of Sciences, Seminar Room 424/8.

(Light refreshments will be served at 13:45)