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arXiv:0908.1986 · Journal of Physics A Mathematical and Theoretical

Criticality and entanglement in random quantum systems

G Refael, Joel E. Moore

Published Dec 2, 2009• 100 citations
arXivHTMLPDF

Abstract

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random (‘pure’) quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.

DOI
10.1088/1751-8113/42/50/504010

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A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to compute the entanglement entropy of (2+1)(2+1)(2+1)-dimensional quantum critical points with randomness, from a conceptual angle where the quenched disorder can be considered as dimensionally reducible interactions. As a concrete example, we reveal novel entanglement signatures of (2+1)(2+1)(2+1)-dimensional Dirac fermion exposed to a random magnetic field, which hosts a class of emergent disordered quantum critical points. We demonstrate that the entanglement entropy satisfies the area-law scaling, and observe a modification of the area-law coefficient that points to the emergent disordered quantum criticality. Moreover, we also obtain the subleading correction to the entanglement entropy due to a finite correlation length. This subleading correction is found to be a universal function of the correlation length and disorder strength. We discuss its connection to the renormalization group flows of underlying theories.
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Abstract We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent L, the points of which with probability p belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as a(p)LD, where a(p) is a non-universal function, to which there is a logarithmic correction term, b(p)LD−1 ln L. In 1D the prefactor is given by b(p)=c/3f(p), where c is the central charge of the model and f(p) is a universal function. In 2D the prefactor has a different functional form of p below and above the percolation threshold. Graphical abstract