Thermalization of dilute impurities in one dimensional spin chains
- URL: http://arxiv.org/abs/2105.09348v4
- Date: Wed, 5 Apr 2023 01:06:28 GMT
- Title: Thermalization of dilute impurities in one dimensional spin chains
- Authors: Dries Sels and Anatoli Polkovnikov
- Abstract summary: We analyze a crossover between ergodic and non-ergodic regimes in a spin chain with a dilute density of impurities.
We propose a mechanism for the delocalization of these impurities in the thermodynamic limit.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We analyze a crossover between ergodic and non-ergodic regimes in an
interacting spin chain with a dilute density of impurities, defined as spins
with a strong local field. The dilute limit allows us to unravel some finite
size effects and propose a mechanism for the delocalization of these impurities
in the thermodynamic limit. In particular we show that impurities will always
relax by exchanging energy with the rest of the chain. The relaxation rate only
weakly depends on the impurity density and decays exponentially, up to
logarithmic corrections, with the field strength. We connect the relaxation to
fast operator spreading and show that the same mechanism destabilizes the
recursive construction of local integrals of motion at any impurity density. In
the high field limit, impurities will appear to be localized, and the system
will be non-ergodic, over a wide range of system sizes. However, this is a
transient effect and the eventual delocalization can be understood in terms of
a flowing localization length.
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