Quantum spin chains with multiple dynamics*

Many-body systems with multiple emergent time scales arise in various contexts, including correlated quantum materials and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitation has a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a field theory and determine various correlation functions and entanglement properties, as well as an exact mapping to the non-equilibrium dynamics of a classical spin chain. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.