Shape dependence of two-cylinder Rényi entropies for free bosons on a lattice

Abstract

Universal scaling terms occurring in Rényi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different ansatzes. Although none of these ansatzes are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the AdS/CFT correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.

Holographic torus entanglement and its renormalization group flow

“…4). This singular behavior is not generic, and for instance is absent in the free scalar [45,46,53] and Dirac fermion [44] CFTs, at the large-n O(n) Wilson-Fisher fixed point [46], and in the so-called Extensive Mutual Information model [45]. It would be interesting to see to what extent it becomes smoothed out by including 1/N corrections.…”

Cubic trihedral corner entanglement for a free scalar

“…1 Despite this challenge, the many different types of geometric features available in higher-dimensional entangling surfaces offers a rich opportunity to search for new universal quantities in the entanglement entropy. [2][3][4][5][6][7] In addition to giving information about features of the underlying critical theory, understanding these quantities in free theories is a necessary precursor to their exploration in interacting critical points, 8,9 such as those in real quantum materials or atomic systems. [10][11][12][13] In this paper, we examine a particular universal quantity that arises in d = 3 + 1 spacetime dimensions when the entangling geometry contains a (cubic) trihedral corner -see Fig.…”

Universal divergence of the Rényi entropy of a thinly sliced torus at the Ising fixed point

“…The numerical value of κ n has previously been calculated in a number of free theories, holographic duals, and phenomenological models. [19][20][21][22][23] Specifically, values of κ for the free scalar field theory in 2 + 1 are κ 1,Gaussian = 0.0397 for the von Neumann entropy 11 and κ 2,Gaussian = 0.0227998 for the second Rényi entropy S 2 (A). 7 This second value κ 2,Gaussian is of particular relevance to the present study.…”

“…7 To put this result into context, we can compare our estimate to that obtained in Ref. 19, which also aims to numerically extract κ 2,Gaussian but does not take into account the proposed offset that scales as γ . Although the authors were able to collect a dataset for system sizes as large as L/δ = 2000, their extrapolation to the thermodynamic limit yielded a value for κ 2,Gaussian that is still 9% off from its theoretical value.…”

“…Contrary to the recent efforts described above to study a corner's universal contribution to the Rényi entropy in both free and interacting theories, studies of κ have been relatively restricted, with results obtained only for free theories and theories with a gravitational dual. The cases where κ has been studied include the free scalar field theory with the dynamical exponent z = 1 7,11,19,20 and z = 2 (the quantum Lifshitz model), 21,22 as well as their fermionic analogues: Dirac fermions with z = 1 7,11,23 and z = 2 (the quadratic band touching model). 22,23 For CFTs in 2 + 1, the universal coefficient κ is known to be rigorously related to the universal corner coefficient through an exact conformal mapping in the thin-slice and small-angle limit of the cylindrical and corner geometries, respectively.…”