Berislav Buca

Non-stationary quantum many-body dynamics: chaos, conservation laws and dynamical symmetries

The assumption that quantum systems relax to a stationary (time-independent) state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. However, real-world phenomena, from life to weather patterns are persistently non-stationary. We will discuss simple algebraic conditions that prevent a quantum many-body system from ever reaching a stationary state, not even a non-equilibrium one. I call these algebraic conditions dynamical symmetries. This unusual state of matter, characterized by persistent oscillations, has been recently called a time crystal. Based on examples we will argue that persistent periodic motion is unrelated to integrability in the quantum case. We show that its existence can be even, counter-intuitively, induced through the dissipation itself. We give several physically relevant examples in both closed and open quantum many-body systems, including an isolated XXZ spin chain that for which the frequency of the persistent oscillations is fractal function of the interaction strength, a quasi-1D magnet with attractor-like dynamics, and a spin-dephased Fermi-Hubbard model. We will show that, remarkably, the second of these models has an infinite set of conservation laws, but still has level repulsion in the spectrum bringing into question the relation between conservation laws, chaos, and persistent time-periodic dynamics.

References:
B Buca, J Tindall, D Jaksch. Nat. Comms. 10 (1), 1730 (2019)
M Medenjak, B Buca, D Jaksch. arXiv:1905.08266 (2019)
B Buca, D Jaksch. Phys. Rev. Lett. 123, 260401 (2019)
J Tindall, B Buca, J R Coulthard, D Jaksch. Phys. Rev. Lett. 123, 030603 (2019)
J Tindall, C Sanchez Munoz, B Buca, D Jaksch. New J. Phys. 22 013026 (2020)
C Booker, B Buca, D Jaksch. arXiv:2005.05062 (2020)
B Buca et al. arXiv:2008.11166 (2020)
Dogra, et al. Science, 366, 1496 (2019)