Entanglement and mutual information in two-dimensional nonrelativistic field theories

TL;DR

The paper investigates entanglement entropy in (1+1)-dimensional nonrelativistic CFTs with Lifshitz and Galilean conformal symmetries using holography. It derives a novel $Lif_2$ EE formula for Lifshitz theories at zero and finite temperature, reveals structural similarities with FSC entanglement, and proposes a Lif$_2$ anomaly coefficient inferred from GCFT data. The analysis centers on Lifshitz spacetimes within New Massive Gravity (NMG), including asymptotically Lifshitz vacua and black holes, and introduces central charges $c_{LL}$ and $c_{LX}$ as functions of the dynamical exponent $\nu$. The work also maps out mutual-information phase transitions in these nonrelativistic theories, showing phase boundaries controlled by ratios of central charges and highlighting potential nonunitarity effects in Lifshitz-like regimes, with implications for nonrelativistic holography and condensed-matter applications.

Abstract

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.

Figures (3)

• Figure 1: The Ryu-Takayanagi prescription; $A$ is the entangling region, and $\Sigma$ is the extremal surface in the asymptotically AdS background, where we have used the map $r \to \arctan (r)$ to compactify the radial coordinate.
• Figure 2: Possible minimal surfaces encoding the entanglement entropy for $S_{A\cup B}$, where we used $r \to \arctan (r)$ to compactify the radial coordinate.
• Figure 3: Mutual information phase diagram for $\rm{GCFT}_2$, where $(\sigma, \gamma)$ are defined by Eq. \ref{['dimensionless']}, and ${\cal X}=c_{LM}/c_{LL}$. In the above figure, the gray areas have non-vanishing mutual information and we consider different values of the ratio ${\cal X}$, $0={\cal X}_1<{\cal X}_2<{\cal X}_3$.