Low-energy Fock-space localization for attractive hard-core particles in disorder
Mathematical Physics
2017-06-22 v4 Disordered Systems and Neural Networks
math.MP
Spectral Theory
Abstract
We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is suggested by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. The proof relies on an energetically motivated Combes-Thomas estimate and an effective one-particle analysis. As an application, we show the exponential decay of the two-point function in the infinite system uniformly in the particle number.
Keywords
Cite
@article{arxiv.1703.02465,
title = {Low-energy Fock-space localization for attractive hard-core particles in disorder},
author = {Vincent Beaud and Simone Warzel},
journal= {arXiv preprint arXiv:1703.02465},
year = {2017}
}
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24 pages