Exact dynamics in dual-unitary quantum circuits

Piroli, Lorenzo (author), Bertini, Bruno (author), Cirac, J. Ignacio (author), Prosen, Tomaž (author)

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
• UDC: 536.93
• ISSN on article: 2469-9950
• DOI: 10.1103/PhysRevB.101.094304
• COBISS.SI-ID: 23769347
• Publication date in RUL: 28.07.2020

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

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