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Eigenstate thermalization and many body localization in the random field Heisenberg chain

David Luitz, University of Illinois

27.11.2015 at 09:00 

I will present our recent large-scale exact diagonalization study [1] of the random field quantum Heisenberg chain, which shows the existence of a many body mobility edge. This result is obtained by a careful finite size scaling analysis of various quantities, such as the entanglement entropy, the level statistics and also the Shannon-Renyi entropy, which quantifies the picture of localization in Hilbert space. At weak disorder strength, eigenstate thermalization is fulfilled and local observables are a smooth function of energy in the thermodynamic limit, while eigenstates exhibit a volume law entanglement entropy. However, this breaks down at strong disorder strength where eigenstates have area law entanglement and large fluctuations in local observables of adjacent eigenstates. In the second part of the talk, I will present results obtained by exact time evolution of initial product states in this system, where the exponent of the power law growth with time of the entanglement entropy suggests anomalous diffusion in a large region of the ergodic phase, confirmed by similar behavior of the decay of the spin imbalance relative to the initial state.

[1] "Many-body localization edge in the random-field Heisenberg chain" David J. Luitz, Nicolas Laflorencie, and Fabien Alet Phys. Rev. B 91, 081103(R)

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