Connections between classical mean field models with glassy dynamics and quantum SYK models

Félix Ritort

Jorge Kurchan B

Glassy dynamics have time-reparametrization `softness': glasses fluctuate, and respond to external perturbations, primarily by changing the pace of their evolution. Remarkably, the same situation also appears in toy models of quantum field theory such as the Sachdev-Ye-Kitaev (SYK) model, where the excitations associated to reparametrizations play the role of an emerging `gravity'. I describe here how these two seemingly unrelated systems share common features, arising from a technically very similar origin. This connection is particularly close between glassy dynamics and supersymmetric variants of the SYK model, which I discuss in some detail. Apart from the curiosity that this correspondence naturally arouses, there is also the hope that developments in each field may be useful for the other.

Etienne Granet, Yuta Kikuchi, Henrik Dreyer +1 more

Abstract The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated quantum system that shows a strong signature of quantum chaos. Due to its chaotic nature, the simulation of real-time dynamics becomes quickly intractable by means of classical numerics, and thus, quantum simulation is deemed to be an attractive alternative. Nevertheless, quantum simulations of the SYK model on noisy quantum processors are severely limited by the complexity of its Hamiltonian. In this work, we simulate the real-time dynamics of a sparsified version of the SYK model with 24 Majorana fermions on a trapped-ion quantum processor. We adopt a randomized quantum algorithm, TETRIS, and develop an error mitigation technique tailored to the algorithm. Leveraging the hardware’s high-fidelity quantum operations and all-to-all connectivity of the qubits, we successfully calculate the Loschmidt amplitude for sufficiently long times so that its decay is observed. Based on the experimental and further numerical results, we assess the future possibility of larger-scale simulations of the SYK model by estimating the required quantum resources. Moreover, we present a scalable mirror-circuit benchmark based on the randomized SYK Hamiltonian and the TETRIS algorithm, which we argue provides a better estimate of the decay of fidelity for local observables than standard mirror-circuits.

László Erdős, Benjamin Schlein

Leticia F. Cugliandolo, Gustavo Sergio Lozano, H. Lozza

Leticia F. Cugliandolo, Gustavo Sergio Lozano, H. Lozza

We apply the Kovacs experimental protocol to classical and quantum p-spin models. We show that these models have memory effects as those observed experimentally in super-cooled polymer melts. We discuss our results in connection to other classical models that capture memory effects. We propose that a similar protocol applied to quantum glassy systems might be useful to understand their dynamics. 1 1