20.500.12556/RUL-125581 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 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. quantum physics statistical physics kvantna fizika statistična fizika true false false Angleški jezik Slovenski jezik Neznano 2021-03-26 08:36:23 2021-03-26 08:36:24 2022-09-05 03:51:30 0000-00-00 00:00:00 2021 0 0 Str. 011022-1-011022-30 iss. 1 Vol. 11 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 536.93 2160-3308 10.1103/PhysRevX.11.011022 57287683 19686152 RAZ_Kos_Pavel_2021.pdf RAZ_Kos_Pavel_2021.pdf 1 CE150958D4FB4657315F6AC7E5DF4EA7 9d73f4b45c297f041b9be10bc1fd79c2f9f4f88c6b8ed9ee0f175b26427fee42 bd70277d-a1bb-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=141361 https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011022 1 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=141362 Fakulteta za matematiko in fiziko 0 0 0