Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula

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 ar...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Pavel Kos, Bruno Bertini, Tomaž Prosen
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b60e2cfaf32a423096fc1efc45583913
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b60e2cfaf32a423096fc1efc45583913
record_format	dspace
spelling	oai:doaj.org-article:b60e2cfaf32a423096fc1efc455839132021-12-02T14:37:47ZCorrelations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula10.1103/PhysRevX.11.0110222160-3308https://doaj.org/article/b60e2cfaf32a423096fc1efc455839132021-02-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011022http://doi.org/10.1103/PhysRevX.11.011022https://doaj.org/toc/2160-3308Interacting 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.Pavel KosBruno BertiniTomaž ProsenAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011022 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Pavel Kos Bruno Bertini Tomaž Prosen Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
description	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.
format	article
author	Pavel Kos Bruno Bertini Tomaž Prosen
author_facet	Pavel Kos Bruno Bertini Tomaž Prosen
author_sort	Pavel Kos
title	Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
title_short	Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
title_full	Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
title_fullStr	Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
title_full_unstemmed	Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
title_sort	correlations in perturbed dual-unitary circuits: efficient path-integral formula
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/b60e2cfaf32a423096fc1efc45583913
work_keys_str_mv	AT pavelkos correlationsinperturbeddualunitarycircuitsefficientpathintegralformula AT brunobertini correlationsinperturbeddualunitarycircuitsefficientpathintegralformula AT tomazprosen correlationsinperturbeddualunitarycircuitsefficientpathintegralformula
_version_	1718390974020845568

Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula

Ejemplares similares