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Science China Physics Mechanics and Astronomy

Typical universal entanglers

Feng Wang, Ming‐Xing Luo, Xiu‐Bo Chen, Yixian Yang, Xiaojun Wang

Published Jul 22, 2014• 2 citations
Publisher
DOI
10.1007/s11433-014-5524-z

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This article studies entanglement in generic disordered systems and compares the growth of the wave function entanglement with that of the operator entanglement of the unitary evolution operator. The authors find that there is a perfect correspondence between the two when the former is generated from typical initial states, while other initial product states exhibit faster entanglement production. This provides evidence that slow dynamics is a universal precursor of the many-body localization transition.
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems, and the fluctuations are of equal order. We derive the novel entanglement spectrum that has infinite support in the complex plane and strong energy dependence. We provide evidence of universality, and similar behavior is found in the non-Hermitian Sachdev-Ye-Kitaev model, indicating the general applicability of the Ginibre ensemble to dissipative many-body quantum chaos.
We introduce the (logarithmic) bipartite fidelity of a quantum system as the (logarithm of the) overlap between its ground state wavefunction and the ground state that one would obtain if the interactions between two complementary subsystems A and B were switched off. We argue that it should typically satisfy an area law in dimension d > 1. In the case of one-dimensional quantum critical points (QCP) we find that it admits a universal scaling form, , where is the typical size of the smaller subsystem. The prefactor is proportional to the central charge c and depends on the geometry. We also argue that this quantity can be useful for locating quantum phase transitions, allows for a reliable determination of the central charge, and in general exhibits various properties that are similar to the entanglement entropy. Like the entanglement entropy, it contains subleading universal terms in the case of a 2D conformal QCP.