Many body localization in Heisenberg XXZ magnet in a random field
Marko Znidaric, Tomaz Prosen, Peter Prelovsek
TL;DR
This paper demonstrates that the Heisenberg XXZ spin-1/2 chain in a random magnetic field exhibits many-body localization, with efficient tDMRG simulations showing logarithmic entanglement growth and exponential spatial localization at high temperature.
Contribution
It provides numerical evidence of many-body localization in the Heisenberg XXZ model with random fields, highlighting efficient simulation methods and localization properties.
Findings
tDMRG simulations are efficient with linear matrix dimension growth
Entanglement entropy increases logarithmically over time
Spin-spin correlations show exponential decay indicating localization
Abstract
We numerically investigate Heisenberg XXZ spin-1/2 chain in a spatially random static magnetic field. We find that tDMRG simulations of time evolution can be performed efficiently, namely the dimension of matrices needed to efficiently represent the time-evolution increases linearly with time and entanglement entropies for typical chain bipartitions increase logarithmically. As a result, we show that for large enough random fields infinite temperature spin-spin correlation function displays exponential localization in space indicating insulating behavior of the model.
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