The research of the project ConsQuanDyn focuses on the quantum dynamics of strongly correlated many-body systems with constraints that arise from geometric frustration and strong interactions. Our work in the past reporting period has focused on our three central objectives and we made important progress on all of them:
(a) Constrained hydrodynamic transport
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics of a few conserved quantities emerges universally in the evolution of any complex quantum system, as strong interactions entangle and effectively mix local degrees of freedom. In this project, we studied how constraints can modify transport. We investigated fractonic quantum matter in which the total charge and in addition the total dipole moment are conserved. We found that ergodic systems with these constraints can escape the conventional scenario of diffusive transport, and display subdiffusive relaxation instead. This unconventional transport has also been experimentally explored in quantum simulators of ultracold atoms subjected to a tilted optical lattice or arises in the relaxation dynamics of the lowest Landau level in quantum Hall systems.
(b) Information scrambling and operator growth in constrained spaces
We have shown, that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we studied operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton system. We have identified a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase of operator growth. This critical point is tied to an underlying localization transition, and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We, furthermore, evaluated entanglement properties and the quantum information structure of two-dimensional lattice gauge theories which are highly constrained due to the Gauss law. We focused on how higher-from symmetries can be used to elucidate these phases of matter. We have also developed an information theoretic perspective on the emergence of higher-form symmetries and found that the confining and Higgs phase are separated in 2+1D lattice gauge theories by information theoretic transitions, albeit they are adiabatically connected thermodynamically.
(c) Characterizing exotic phases with constraints
Many-body systems with gauge constraints can lead to unconventional phases of matter with topological order. Examples are fractional quantum Hall states and quantum spin liquids. We have developed a quantum algorithm to realize a quantum spin liquid on a superconducting quantum information processor, have simulated anyon braiding and showed how to measure the topological entanglement entropy of the wave function. We have perturbed the fixed point wave function and explored the phase diagram of a 2+1D lattice gauge theory. There, we explored string dynamics on quantum processors and developed numerical tools to probe the roughening transition in the confining phase. We have also analyzed relaxation and thermalization in periodically driven quantum systems and have found a new fractionalized Floquet prethermal regime. In systems with fractionalized excitations the effective Hamiltonian cannot be obtained by a simple high-frequency expansion, as fractionalized excitations couple in general differently to a drive.
Several of our theoretical predictions have been exploited with quantum processors, quantum simulators, as well as quantum materials and thereby been experimentally explored. We have also published manuscripts and uploaded them onto a preprint server for disseminating our results. In summary, with the project ConsQuanDyn, we could further develop the field and improve our understanding of constraint quantum dynamics in quantum many-body systems.
