Corner contribution to the entanglement entropy of strongly interacting O(2) quantum critical systems in 2+1 dimensions

Abstract

In a D = 2+1 quantum critical system, the entanglement entropy across a boundary with a corner contains a subleading logarithmic scaling term with a universal coefficient. It has been conjectured that this coefficient is, to leading order, proportional to the number of field components N in the associated O(N ) continuum φ 4 field theory. Using density matrix renormalization group calculations combined with the powerful numerical linked cluster expansion technique, we confirm this scenario for the O(2) Wilson-Fisher fixed point in a striking way, through direct calculation at the quantum critical points of two very different microscopic models. The value of this corner coefficient is, to within our numerical precision, twice the coefficient of the Ising fixed point. Our results add to the growing body of evidence that this universal term in the Rényi entanglement entropy reflects the number of low-energy degrees of freedom in a system, even for strongly interacting theories.

Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

“…The von Neumann and Rényi entropies for the free boson Hamiltonian of Eq. (24) can be written in terms of the eigenvalues λ i of the matrix C A as…”

“…Numerical methods for evaluating these correlators are a useful alternative to analytical integration techniques in the continuum 31,32 , particularly in higher space-time dimensions, where high-precision analytical calculations may become infeasible (or impossible). We perform our calculations on the square lattice with a finite number of lattice sites N , motivated by the setup for interacting theories in two dimensions 21,22,24 . Similar calculations have previously been performed at special angles in Ref.…”

“…An alternative strategy to the direct approach 21,22,24,33 is to perform finite-size scaling with the numerical linked-cluster expansion (NLCE). In addition to systematically accessing the limit L, → ∞, the NLCE eliminates the area-law piece and O(1/L) corrections to the Rényi entropy, providing direct access to the corner coefficient.…”

“…Recent numerical work on the interacting quantum critical theories that arise in the 2d Ising, XY and Heisenberg models [20][21][22][23][24][25] suggests that this corner coefficient provides a measure of the low energy degrees of freedom of the critical theory. Partially motivated by these developments, Refs.…”

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

“…Besides the analysis of the corner functionsf (θ) for specific quantum field theories [28][29][30][31][32], many interesting results have been obtained in particular lattice models [34][35][36][37][38][39].…”