Dynamics of anisotropic spin-1 chains with tunable symmetry

The far-from-equilibrium dynamics of interacting quantum systems have been the subject of extensive research in recent years. Numerous non-equilibrium phenomena, including many-body scars, Hilbert space fragmentation, dynamical quantum phase transitions, and time crystals, have been experimentally realized thanks to the quick development of quantum simulators. In this study we employ time-evolving block decimation to study the time evolution of excited initial states of an anisotropic spin-1 Heisenberg Hamiltonian in which the underlying symmetry can be tuned from SU(2) to SU(3) by controlling the contribution from quadrupolar interactions. We analyze the dynamics of the local magnetization, entanglement entropy, fidelity, and spin correlation functions under different degrees of anisotropy. We observe that the degree and rate of thermalization can be controlled via the strength of the quadrupolar terms and discuss the associated conservation laws under which certain initial states display non-thermalizing correlation functions. We conclude that tuning the underlying symmetry provides a powerful knob to control the non-equilibrium dynamics of many-body spin systems.