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2017

Lifshitz entanglement entropy from holographic cMERA

Gentle, Simon A., Vandoren, Stefan

Understand

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA).

In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$.
We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension.
We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow.

Built on

C. Holzhey, F. Larsen, and F. Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nucl. Phys
1994
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech
2004
Earlier work this paper cites.
H. Casini and M. Huerta, “A Finite entanglement entropy and the c-theorem,” Phys. Lett
2004
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement and alpha entropies for a massive scalar field in two dimensions,” J. Stat. Mech
2005
Earlier work this paper cites.
E. Fradkin and J. E. Moore, “Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum,” Phys. Rev. Lett
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP
2006
Earlier work this paper cites.
G. Vidal, “Entanglement Renormalization,” Phys. Rev. Lett
2007
Earlier work this paper cites.
S. Kachru, X. Liu, and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev
Original
2008
Earlier work this paper cites.
G. Vidal, “Class of Quantum Many-Body States That Can Be Efficiently Simulated,” Phys. Rev. Lett
2008
Earlier work this paper cites.
B. Hsu, M. Mulligan, E. Fradkin, and E.-A. Kim, “Universal entanglement entropy in 2D conformal quantum critical points,” Phys. Rev
Original
2009
Earlier work this paper cites.