Power-law entanglement growth from typical product states

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. σz 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 disorderdependent 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. arXiv:1908.07010v1 [cond-mat.dis-nn]

Absence of slow particle transport in the many-body localized phase

“…The existence of l-bits predicts the absence of particle transport and thermalization in the MBL phase, but also an unbounded logarithmic growth of the bipartite entanglement entropy [9,19,[21][22][23][24][25] up to a nonthermal, extensive, saturation value. This behavior is in stark contrast with the thermal phase, where the entanglement entropy grows as a power law in time [26,27]. Without disorder, a linear growth of the entanglement entropy is typically observed [28].…”

Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

“…A number of numerical studies demonstrated later, that for one-dimensional systems with bounded energy density, transport in the delocalized phase is subdiffusive, and thus conductivity in the thermodynamic limit vanishes through the entire phase diagram [10][11][12][13][14]. In addition to the anomalous transport, the delocalized phase shows sublinear growth of entanglement entropy [13,15,16], suppressed spreading of entanglement [17][18][19], intermediate statistics of eigenvalue spacing [20] and satisfies only a modified version of the eigenstates thermalization hypothesis (ETH) [21] (see [22] for a detailed review of the properties of the delocalized phase). A phenomenological explanation of the anomalous dynamical properties of the delocalized phase, based on rare blocking regions, was provided in Refs.…”

Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium

“…The problem can be mapped to a weakly interacting Majorana fermion model coupled to a static Z 2 gauge field [20][21][22][23][24][25][26][27][28][29], which for the considered dynamics becomes effectively disordered. In the noninteracting limit, we find that the gauge flux disorder localizes most of the Majorana fermions but fails to freeze the metallic and critical modes, leading to the observed subdiffusive dynamics although the system is overall nonergodic [30][31][32][33][34]. We identify the subdiffusive dynamics both in an algebraic spread of quantum correlations and the power-law growth of entanglement.…”