TY - JOUR

T1 - Localization with random time-periodic quantum circuits

AU - Sünderhauf, Christoph

AU - Pérez-García, David

AU - Huse, David A.

AU - Schuch, Norbert

AU - Cirac, J. Ignacio

N1 - Funding Information:
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through the ERC Starting Grant WASCOSYS (No. 636201), the ERC Consolidator Grant GAPS (No. 648913), and the ERC Advanced Grant QENOCOBA (No. 742102). D.P.G. acknowledges financial support of Severo Ochoa project SEV-2015-556 funded by MINECO.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/10/30

Y1 - 2018/10/30

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevB.98.134204

DO - 10.1103/PhysRevB.98.134204

M3 - Article

AN - SCOPUS:85056403985

SN - 2469-9950

VL - 98

JO - Physical Review B

JF - Physical Review B

IS - 13

M1 - 134204

ER -