Typicality approach to the optical conductivity in thermal and many-body 
localized phases

Steinigeweg, Robin; Herbrych, Jacek; Pollmann, Frank; Brenig, Wolfram

doi:10.1103/PhysRevB.94.180401

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Typicality approach to the optical conductivity in thermal and many-body localized phases

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Pollmann, Frank
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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https://arxiv.org/pdf/1512.08519.pdf
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Steinigeweg, R., Herbrych, J., Pollmann, F., & Brenig, W. (2016). Typicality approach to the optical conductivity in thermal and many-body localized phases. Physical Review B, 94(18): 180401. doi:10.1103/PhysRevB.94.180401.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002C-0DF3-4

Abstract

We study the frequency dependence of the optical conductivity Re sigma(omega) of the Heisenberg spin-1/2 chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random z-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform Re sigma(omega) for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of Re sigma(omega) is well described by Re sigma(omega) approximate to sigma(dc) + a|omega|(alpha), with alpha approximate to 1 in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of sigma(dc) in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of alpha(dc) is consistent with the existence of a mobility edge.