Localization with random time-periodic quantum circuits

Christoph Sünderhauf, David Pérez-García, David A. Huse, Norbert Schuch, J. Ignacio Cirac

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42 Scopus citations


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.

Original languageEnglish (US)
Article number134204
JournalPhysical Review B
Issue number13
StatePublished - Oct 30 2018

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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