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Localization with random time-periodic quantum circuits

Author(s): Suenderhauf, Christoph; Perez-Garcia, David; Huse, David A; Schuch, Norbert; Ignacio Cirac, J

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Abstract: We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each time step is repeated with the same random instances. We obtain analytical results for arbitrary local Hilbert space dimension d; on a single site, average time evolution acts as a depolarising channel. In the spin 1/2 (d = 2) case, this is further quantified numerically. For that, we develop a new numerical method that reduces complexity by an exponential factor. Haar-distributed unitaries lead to full depolarization after many time steps, i.e., local thermalization. A unitary probability distribution with tunable coupling strength allows us to observe a many-body localization transition. In addition to a spin chain under a unitary circuit, we consider the analogous problem with Gaussian circuits. We can make stronger statements about the entire covariance matrix instead of single sites only, and find that the dynamics is localizing. For a random time evolution operator homogeneous in space, however, the system delocalizes.
Publication Date: 1-Oct-2018
Electronic Publication Date: 30-Oct-2018
Citation: Suenderhauf, Christoph, Perez-Garcia, David, Huse, David A, Schuch, Norbert, Ignacio Cirac, J. (2018). Localization with random time-periodic quantum circuits. PHYSICAL REVIEW B, 98 (10.1103/PhysRevB.98.134204
DOI: doi:10.1103/PhysRevB.98.134204
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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