Localization in the random XXZ quantum spin chain
- URL: http://arxiv.org/abs/2210.14873v3
- Date: Fri, 26 Jan 2024 00:21:55 GMT
- Title: Localization in the random XXZ quantum spin chain
- Authors: Alexander Elgart, Abel Klein
- Abstract summary: We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$frac12$ chain in a random magnetic field.
We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space.
- Score: 55.2480439325792
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the many-body localization (MBL) properties of the Heisenberg XXZ
spin-$\frac12$ chain in a random magnetic field. We prove that the system
exhibits localization in any given energy interval at the bottom of the
spectrum in a nontrivial region of the parameter space. This region, which
includes weak interaction and strong disorder regimes, is independent of the
size of the system and depends only on the energy interval. Our approach is
based on the reformulation of the localization problem as an expression of
quasi-locality for functions of the random many-body XXZ Hamiltonian. This
allows us to extend the fractional moment method for proving localization,
previously derived in a single-particle localization context, to the many-body
setting.
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