Correlations in perturbed dual-unitary circuits: efficient path-integral formula

Kos, Pavel (author), Bertini, Bruno (author), Prosen, Tomaž (author)

Interacting many-body systems with explicitly accessible spatiotemporal correlation functions are extremely rare, especially in the absence of Bethe-ansatz or Yang-Baxter integrability. Recently, we identified a remarkable class of such systems and termed them dual-unitary quantum circuits. These are brickwork-type local quantum circuits whose dynamics are unitary in both time and space. The spatiotemporal correlation functions of these systems turn out to be nontrivial only at the edge of the causal light cone and can be computed in terms of one-dimensional transfer matrices. Dual unitarity, however, requires fine-tuning, and the degree of generality of the observed dynamical features remains unclear. Here, we address this question by studying perturbed dual-unitary quantum circuits. Considering arbitrary perturbations of the local gates, we prove that for a particular class of unperturbed elementary dual-unitary gates the correlation functions are still expressed in terms of one-dimensional transfer matrices. These matrices, however, are now contracted over generic paths connecting the origin to a fixed end point inside the causal light cone. The correlation function is given as a sum over all such paths. Our statement is rigorous in the “dilute limit,” where only a small fraction of the gates is perturbed, and in the presence of random longitudinal fields, but we provide theoretical arguments and stringent numerical checks supporting its validity even in the clean case (no randomness) and when all gates are perturbed. As a by-product of our analysis, in the case of random longitudinal fields—which turns out to be equivalent to certain classical Markov chains—we find four types of non-dual-unitary (and nonintegrable) interacting many-body systems where the correlation functions are exactly solvable and given—without approximations—by the path-sum formula.

• Language: English
• Keywords: quantum physics, statistical physics
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 011022-1-011022-30
• Numbering: Vol. 11, iss. 1
• PID: 20.500.12556/RUL-125581
• UDC: 536.93
• ISSN on article: 2160-3308
• DOI: 10.1103/PhysRevX.11.011022
• COBISS.SI-ID: 57287683
• Publication date in RUL: 26.03.2021

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., X
• Publisher: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

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: 26.03.2021

Secondary language

• Language: Slovenian
• Keywords: kvantna fizika, statistična fizika

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