Universal entanglement entropy in two-dimensional conformal quantum critical points

Abstract

We study the scaling behavior of the entanglement entropy of two-dimensional conformal quantum critical systems, i.e., systems with scale-invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that under quite general conditions, the entanglement entropy of a large and simply connected subsystem of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory

Left-right entanglement entropy of boundary states

“…The results have some resemblance to the calculations presented in [29], even though the context is quite different.…”

Notes on quantum entanglement of local operators

“…It is a useful tool when we investigate the distinctive features of various quantum states. For example, it gives us the method of classifying the quantum structure of several states in condensed matter physics, e.g., [1][2][3][4][5][6][7]. The quantum entanglement is expected to be an important quantity which may shed light on the mechanism behind the AdS/CFT correspondence, e.g., [8][9][10][11].…”

“…Here Σ 1 is usual d + 1 dimensional Euclidean space. 3 Here only one operator acts on the ground state. However the result in (2.14) can be generalized to that for the excited state defined by acting various operators on the ground state as we will explain later.…”

Entanglement entropy: a perturbative calculation

“…3 The entangling surface is chosen to be some general (d − 2)-dimensional surface Σ. Our notation for the rest of the paper is summarized in appendix A.…”

“…Entanglement entropy is a rapidly developing technique in condensed matter physics [1][2][3][4][5] and holography [6,7]. One of the main theoretical gaps that substantially limits its studies is the paucity of computational tools.…”