Almost Universal Behavior in Many-Body Hamiltonians

Adhip Agarwala

Christopher M. Langlett, Joaquin F. Rodriguez-Nieva

Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory (RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing "coarse" features of many-body quantum Hamiltonians in chaotic regimes, such as the Wigner-Dyson level spacing statistics or the volume-law behavior of eigenstate entanglement entropy, it remains a challenge to describe their "finer" features, particularly those arising from spatial locality. Here, we show that we can accurately describe the statistical behavior of eigenstate ensembles in many-body Hamiltonians by using pure random states with physical constraints that capture the essential features of the Hamiltonian, specifically spatial locality and symmetries. We demonstrate our approach on local spin Hamiltonians with a scalar U(1) charge. By constructing ensembles of constrained random states that account for two commuting scalar charges playing the role of energy and magnetization, we describe the patterns of entanglement of midspectrum eigenstates beyond their average volume-law behavior, including O(1) corrections and fluctuations, analytically and numerically. When defining the correspondence between quantum chaotic eigenstates in many-body Hamiltonians and RMT ensembles, our work highlights the important role played by spatial locality in describing universal features beyond the volume-law behavior.

Jean-Louis Basdevant, André Martin, J. M. Richard

Bertrand Evrard, An Qu, Jean Dalibard +1 more

The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin-1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the nonlinearity of the spectrum leads to irreversibility, characterized by a universal behavior. When the integrability of the Hamiltonian is broken, a chaotic dynamics emerges and leads to thermalization, in agreement with the eigenstate thermalization hypothesis paradigm.

Charles Stahl, Ethan Lake, Vedika Khemani

Active systems can exhibit a broad range of phenomena forbidden in equilibrium. Their dynamics are often specified by abstract local update rules, and it is generally unclear when the same behavior can arise from physically natural driving. Here we show that two simple driving mechanisms can universally simulate any local active dynamics in spin systems. The first is the familiar setting of a time-periodic Hamiltonian coupled to a cold bath, which we call a "many-body Brownian pump." As a second mechanism, we promote the Brownian ratchet, traditionally a mechanism for transport, to a "many-body Brownian ratchet": a static Hamiltonian coupled to a hot bath and a cold bath, where the resulting steady heat current can be harnessed not only to drive transport but also to generate local active dynamics. Using probabilistic cellular automata as an explicit model, we prove that for any continuous-time (or discrete-time) local active dynamics, there is always a many-body Brownian ratchet (or pump) that approximates the dynamics, up to noise that can be made arbitrarily weak by tuning energy scales and other parameters. As a concrete demonstration, we construct a simple ferromagnetic Ising ratchet on a bilayer lattice. When the two layers are coupled to baths at different temperatures, this model serves as a robust classical memory even under a symmetry-breaking field, something impossible in equilibrium. More broadly, our work shows that ratchets can use steady heat currents to autonomously generate and stabilize novel collective behavior, realizing a new static setting for nonequilibrium many-body dynamics.

Wei-Zhu Yi, Hao-Jie Lin, Ze-Xun Lin +2 more

The universal dynamical phenomenon of von Neumann entropy plays an important role in understanding the nature of open many-body systems, as it uncovers general collective properties driven by correlation and quantum dynamics. Here, we reveal a universal time evolution behavior of bipartite von Neumann entropy in open quantum systems with dissipation into the surrounding environments. The coupling with the environment leads to a rapid growth of the entropy, resulting in an exotic short-time evolution law, S ( t ) ∼ − t ln t . Such a fast growth behavior is proved to be a general phenomenon for generic many-body systems in dissipative environments, as long as the systems exhibit well-defined fermionic quasiparticles. Interestingly, even for strongly interacting Luttinger liquids, which display vanishing fermionic but emergent bosonic quasiparticles, the same dynamical phenomenon is still found to persist. These results demonstrate a universal Liouvillian dynamical feature that has no counterpart in isolated Hamiltonian systems.