Universal behavior of entanglement in 2D quantum critical dimer models

Abstract

We examine the scaling behavior of the entanglement entropy for the 2D\nquantum dimer model (QDM) at criticality and derive the universal finite\nsub-leading correction $\\gamma_{QCP}$. We compute the value of $\\gamma_{QCP}$\nwithout approximation working directly with the wave function of a generalized\n2D QDM at the Rokhsar-Kivelson QCP in the continuum limit. Using the replica\napproach, we construct the conformal boundary state corresponding to the cyclic\nidentification of $n$-copies along the boundary of the observed region. We find\nthat the universal finite term is $\\gamma_{QCP}=\\ln R-1/2$ where $R$ is the\ncompactification radius of the bose field theory quantum Lifshitz model, the\neffective field theory of the 2D QDM at quantum criticality. We also\ndemonstrated that the entanglement spectrum of the critical wave function on a\nlarge but finite region is described by the characters of the underlying\nconformal field theory. It is shown that this is formally related to the\nproblems of quantum Brownian motion on $n$-dimensional lattices or equivalently\na system of strings interacting with a brane containing a background\nelectromagnetic field and can be written as an expectation value of a vertex\noperator.\n