Journal
PHYSICAL REVIEW B
Volume 98, Issue 13, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.98.134204
Keywords
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Funding
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through the ERC Starting Grant WASCOSYS [636201]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through ERC Consolidator Grant GAPS [648913]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through ERC Advanced Grant QENOCOBA [742102]
- Severo Ochoa project - MINECO [SEV-2015-556]
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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.
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