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arXiv:1803.01064 · Physical review. D/Physical review. D.

Holographic approach to entanglement entropy in disordered systems

Rajesh Narayanan, Chanyong Park B, Yun‐Long Zhang

Published Feb 27, 2019• 10 citations
arXivHTMLPDF

Abstract

We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed point, that is perturbed by weak disorder into a Lifshitz theory at the IR fixed point. Through numerical fitting, we find that the disorder correlations lead to a subleading power-law term in the entanglement entropy that vanishes at the IR fixed point. Interestingly, the exponent that controls the power-law vanishing of the subleading term seems to be almost universal as it depends very weakly on the strength of the disorder. We show that our results can be put in the context of the c-theorem by defining an effective central charge that decreases along the RG flow. We also investigate disorder induced long-range correlations between the two subsystems by studying the holographic mutual information.

DOI
10.1103/physrevd.99.046019

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We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed point, that is perturbed by weak disorder into a Lifshitz theory at the IR fixed point. Through numerical fitting, we find that the disorder correlations lead to a subleading power-law term in the entanglement entropy that vanishes at the IR fixed point. Interestingly, the exponent that controls the power-law vanishing of the subleading term seems to be almost universal as it depends very weakly on the strength of the disorder. We show that our results can be put in the context of the c-theorem by defining an effective central charge that decreases along the RG flow. We also investigate disorder induced long-range correlations between the two subsystems by studying the holographic mutual information.
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Abstract The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time dimensions, and the sphere free energy F in odd dimensions. In this work we study the entanglement entropy on a sphere of radius R in a large radius limit, for field theories with gravity duals. At large radius the entropy admits a geometric expansion in powers of R; the leading term is the well-known area term, and we also consider the subleading contributions. These terms can be physical, they contain information about the full renormalization group flow, and they reproduce known monotonicity theorems in particular cases. We set up an efficient method for calculating them using the Hamilton-Jacobi equation for the holographic entanglement entropy. We first reproduce the known result for the area term, the coefficient multiplying Rd−2 in the entanglement entropy. We then obtain the holographic result for the Rd−4 term and establish its irreversibility. Finally, we derive the Rd−6 coefficient for holographic theories, and also establish its irreversibility. This result goes beyond what has been proved in quantum field theory based on strong subadditivity, and hints towards new methods for analyzing the monotonicity of the renormalization group in space-time dimensions bigger than four.
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We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue that previously proposed random lines of fixed points with Lifshitz scaling in fact flow toward other universal fixed points, and this flow is captured by a ``one-loop'' analysis. Our approach appears best controlled in theories with only a few operators with low scaling dimension. In this regime, we compare our predictions for the flow of disorder to holographic models, and find complete agreement.
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