Collective Modes and Dynamics in Strongly Correlated Many-Body Systems: a Variational Cluster Approach

Enrico Arrigoni

Libo Zhang, Chilong Liu, Guixu Xie +9 more

Collective dynamics in engineered quantum systems offer a unique and versatile platform for exploring how many-body correlations bridge microscopic entanglement and macroscopic behavior. In this work, we report collective Dicke dynamics of acoustic modes in a macroscopic high-overtone bulk acoustic resonator (HBAR). To achieve this, we engineer a hybrid quantum acoustodynamic system comprising an HBAR strongly coupled to a superconducting transmon qubit. The HBAR device is distinctive in the sense that its narrow mode spacing, together with enhanced qubit-mode coupling strength, gives rise to efficient coupling between the transmon and clusters of near-resonant modes. By harnessing the system properties, we observe collective dynamics involving clusters composed by two or three mechanical modes, where their non-resonant spectrum allows for the observation of the transition between the Dicke static regime to dynamically induced timed-Dicke one. The coherent collective behavior of the system is supported by time-domain measurements of the qubit's purity, indicating the quantum nature of the collective dynamics. Overall, our work establishes HBAR-based hybrid quantum system as a promising platform for exploring many-body collective dynamics in macroscopic mechanical systems.

Michael Knap, Wolfgang von der Linden, Enrico Arrigoni

A numerical approach is presented that allows to compute nonequilibrium steady-state properties of strongly correlated quantum many-body systems. The method is imbedded in the Keldysh Green's function formalism and is based upon the idea of the variational cluster approach as far as the treatment of strong correlations is concerned. It appears that the variational aspect is crucial as it allows for a suitable optimization of a ``reference'' system to the nonequilibrium target state. The approach is neither perturbative in the many-body interaction nor in the field, that drives the system out of equilibrium, and it allows to study strong perturbations and nonlinear responses of systems in which also the correlated region is spatially extended. We apply the presented approach to nonlinear transport across a strongly correlated quantum wire described by the fermionic Hubbard model. We illustrate how the method bridges to cluster dynamical mean-field theory upon coupling two baths containing an increasing number of uncorrelated sites.

Maxim Vergeles

Philip Osterholz, Fabio Bensch, Shuanghong Tang +4 more

Strongly interacting many-body systems exhibit collective properties that emerge from complex correlations among microscopic degrees of freedom. These cooperative phenomena govern the non-equilibrium response of quantum systems, with relevance ranging from condensed matter physics to quantum field theories describing fundamental aspects of our universe. Understanding such emergent dynamics from first principles remains one of the central challenges in quantum many-body physics. Here we report on the observation of collective cluster nucleation dynamics following quenches in 2D ferromagnetic quantum Ising systems implemented in an atomic Rydberg array. Our experiments reveal two distinct regimes: In the confined regime, we observe an energy-dependent cluster size, revealing large collective clusters exceeding ten spins. In contrast, the deconfined regime is characterized by kinetically constrained, avalanche-like nucleation dynamics involving the entire system. Our findings establish a new frontier for quantum simulations with Rydberg arrays, enabling controlled exploration of non-equilibrium phenomena previously out of reach. Beyond advancing experimental capabilities, they provide fundamental insights into highly correlated processes with implications that reach from quantum magnetism and glassy dynamics to cosmological models of the early universe.

Erik G. C. P. van Loon