Lattice study of Rényi entanglement entropy in SU(Nc) lattice Yang-Mills theory with N

Abstract

We consider the second Rényi entropy S (2) in pure lattice gauge theory with SU (2), SU (3) and SU (4) gauge groups, which serves as a first approximation for the entanglement entropy and the entropic C-function. We compare the results for different gauge groups using scale setting via the string tension. We confirm that at small distances l our approximation for the entropic C-function C(l), calculated for the slab-shaped entangled region of width l, scales as N 2 c − 1 in accordance with its interpretation in terms of free gluons. At larger distances l C(l) is found to approach zero for Nc = 3, 4, somewhat more rapidly for Nc = 4 than for Nc = 3. This finding supports the conjectured discontinuity of the entropic C-function in the large-N limit, which was found in the context of AdS/CFT correspondence and which can be interpreted as transition between colorful quarks and gluons at small distances and colorless confined states at long distances. On the other hand, for SU (2) gauge group the long-distance behavior of the entropic C-function is inconclusive so far. There exists a small region of lattice spacings yielding results consistent with Nc = 3, 4, while results from other lattice spacings deviate without clear systematics. We discuss several possible causes for discrepancies between our results and the behavior of entanglement entropy in holographic models.

Hamilton-Jacobi formulation of holographic entanglement entropy

“…[17]) show a rapid decrease in a number of effective degrees of freedom over the length scales 0.2 ≤ a ≤ 0.6 fm. A similar behaviour is seen for SU (3) and SU (4) gauge groups [18]. Great aspect of quantities like C(a) is that those are not restricted to cases of non-dynamical quarks, like the Polyakov loops, and in turn are a good candidate of a universal confinement order parameter.…”

“…For finite N we expect the behaviour to be smoothed. Surprisingly, C(a) can be reliably studied in lattice gauge theories [7,17,18]. For example, the results for the d = 3 + 1 SU (2) gauge theory computed on the lattice (see Fig.…”

Wilsonian Effective Action and Entanglement Entropy

“…On the other hand, we have little understanding of EE in general interacting QFTs, apart from exactly solvable cases [20] or some supersymmetric theories [12,13,[21][22][23]. EE in interacting theories are discussed in perturbative [24,25], nonperturbative [26][27][28][29][30][31][32], lattice [33][34][35][36][37], or in terms of variational trial wave functions [28][29][30].…”

Interplay between the holographic QCD phase diagram and mutual & n-partite information

“…It is therefore of great interest to examine how this structure of shared information changes with the size of the subsystem (the length scale), as it might provide important information about the confinement structure. With the exception of a few lattice related papers [44][45][46][47], the discussion of entanglement entropy in QCD like gauge theories has been rather limited. The conceptual as well as computational difficulties presented in the definition of entanglement entropy for interacting field theories make it extremely difficult to get any reliable nonperturbative estimate of the entanglement entropy relevant for QCD.…”