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Published September 19, 2014 | Submitted + Published
Journal Article Open

New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains

Abstract

We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone |x|≤v|t|, we obtain |x|≤v|t|α for some 0<α<1. We can characterize the allowed values of α exactly as those exceeding the upper transport exponent α+u of a one-body Schrödinger operator. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. We also discuss anomalous LR bounds with power-law tails for a random dimer field.

Additional Information

© 2014 American Physical Society. Received 13 August 2014; published 18 September 2014. D. Damanik was supported in part by NSF Grant No. DMS–1067988, M. Lukic was supported in part by NSF Grant No. DMS–1301582, and W. Yessen was supported by NSF Grant No. DMS–1304287. The authors wish to thank a referee for raising some interesting questions.

Attached Files

Published - PhysRevLett.113.127202.pdf

Submitted - 1408.1796v2.pdf

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August 20, 2023
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