Isolated Heisenberg magnet as a quantum time crystal
Physical Review B American Physical Society 102:4 (2020) 041117(R)
Abstract:
We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not equilibrate. It constitutes an example of persistent nonstationarity in a quantum many-body system that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries. We discuss how the ensuing persistent oscillations that seemingly violate one of the most fundamental laws of physics could be observed experimentally.Stationary state degeneracy of open quantum systems with non-abelian symmetries
Journal of Physics A: Mathematical and Theoretical IOP Publishing 53:21 (2020) 215304
Abstract:
We study the null space degeneracy of open quantum systems with multiple non-abelian, strong symmetries. By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of multiple, commuting, invariant subspaces we derive a tight lower bound for the stationary state degeneracy. We apply these results within the context of open quantum many-body systems, presenting three illustrative examples: a fully-connected quantum network, the XXX Heisenberg model and the Hubbard model. We find that the derived bound, which scales at least cubically in the system size the SU(2) symmetric cases, is often saturated. Moreover, our work provides a theory for the systematic block-decomposition of a Liouvillian with non-abelian symmetries, reducing the computational difficulty involved in diagonalising these objects and exposing a natural, physical structure to the steady states—which we observe in our examples.Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss
(2020)
Dissipation induced nonstationarity in a quantum gas
Physical Review Letters American Physical Society 123:26 (2019) 260401
Abstract:
Nonstationary longtime dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, M. Landini, K. Kroeger, L. Hruby, T. Donner, and T. Esslinger, arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable—even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the nonstationary behavior.Quantum synchronisation enabled by dynamical symmetries and dissipation
New Journal of Physics IOP Publishing 22 (2019) 013026