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Exact dynamics in dual-unitary quantum circuits
ID Piroli, Lorenzo (Author), ID Bertini, Bruno (Author), ID Cirac, J. Ignacio (Author), ID Prosen, Tomaž (Author)

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Abstract
We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

Language:English
Keywords:quantum mechanics, nonlinear statistical mechanics
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Author Accepted Manuscript
Year:2020
Number of pages:Str. 094304-1-094304-16
Numbering:Vol. 101, iss. 9
PID:20.500.12556/RUL-117818 This link opens in a new window
UDC:536.93
ISSN on article:2469-9950
DOI:10.1103/PhysRevB.101.094304 This link opens in a new window
COBISS.SI-ID:23769347 This link opens in a new window
Publication date in RUL:28.07.2020
Views:1060
Downloads:296
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Record is a part of a journal

Title:Physical review
Publisher:American Physical Society
ISSN:2469-9950
COBISS.SI-ID:2997348 This link opens in a new window

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:28.07.2020

Secondary language

Language:Slovenian
Keywords:kvantna mehanika, nelinearna statistična mehanika

Projects

Funder:EC - European Commission
Funding programme:H2020
Project number:694544
Name:Open Many-body Non-Equilibrium Systems
Acronym:OMNES

Funder:ARRS - Slovenian Research Agency
Project number:P1-0402
Name:Matematična fizika

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