Abstract
Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy. Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states with the operator entanglement entropy of the unitary evolution operator, while special product states, e.g. $\sigma_z$ basis states, can exhibit faster entanglement production. In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent, and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition.
Highlights
Entanglement is an intrinsic property of quantum manybody wave functions and describes the amount of information a subsystem A contains about its complement B
The doubly logarithmic scale reveals that the growth of both entropies follows a power law tα in time until saturation, and the domain of the
Since the time-evolution operator needs to encode the entanglement production for any initial state, its entanglement entropy can only be expected to grow with a rate similar to that seen in typical wave functions, which are given by initial product states with maximal bond dimension χ and represent an overwhelming majority in the class of all A :: B separable pure states
Summary
Entanglement is an intrinsic property of quantum manybody wave functions and describes the amount of information a subsystem A contains about its complement B. The anomalous thermalization is reflected in a sublinear power-law growth proportional to tα of the wave-function entanglement entropy [65], even in systems which do not have globally conserved densities [66], suggesting that the generic slow dynamics is a universal precursor of MBL. In such pre-MBL systems, the entanglement production exponent α varies continuously with disorder and vanishes at the MBL transition, where the logarithmic growth takes over. V we conclude by summarizing and discussing our main results
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