Universal contributions to entanglement entropy at critical points in two spatial dimensions

Lauren E. Hayward Sierens, Pablo Bueno, Rajiv R. P. Singh +2 more

Samuel L. Braunstein, Saurya Das, S. Shankaranarayanan

Eduardo Fradkin, Joel E. Moore

The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

Chloé Van Bastelaere, Rui-Zhen Huang, Laurens Vanderstraeten

Entanglement scaling provides a powerful probe of universal properties at quantum critical points. In two dimensions, contributions originating from a corner-shaped bipartition exhibit a universal scaling, which is determined by the underlying conformal field theory. We develop a method to extract this corner entanglement entropy from projected entangled pair states directly in the thermodynamic limit. When applied to models at a quantum critical point, we show that the corner contribution exhibits scaling with the effective correlation length, in agreement with the hypothesis of finite-entanglement scaling. Our results for the corner coefficients are consistent with other methods, demonstrating the efficiency of our method for diagnosing strongly-correlated quantum critical points in two dimensions.

William Witczak‐Krempa

The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement entropy changes with small deformations of the entangling surface. This leads to the notion of entanglement susceptibilities. These relate the variation of the EE to the geometric variation of the subregion. We determine the form of the leading entanglement susceptibilities for a large class of scale invariant states, such as the ground states of conformal field theories, and systems with Lifshitz scaling, which includes fixed points governed by disorder. We then use the susceptibilities to derive the universal contributions that arise due to nonsmooth features in the entangling surface: corners in two dimensions, as well as cones and trihedral vertices in three dimensions. We finally discuss the generalization to R\'enyi entropies.

Micheal S. Berger, Roman V. Buniy