Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
arXiv:2504.13258 · doi:10.1103/9cbp-7tvv
Abstract
Non-equilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for non-equilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multi-point correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large- Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and non-local Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large- results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the non-interacting SYK model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting SYK model thermalizes slower than the non-interacting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the non-local and/or multi-point quantum correlations that relax as the system thermalizes.
arXiv comment23 pages, 9 figures
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