Crossing-symmetric twist field correlators and entanglement negativity in minimal CFTs

Abstract

We study conformal twist field four-point functions on a ℤN orbifold. We examine in detail the case N = 3 and analyze theories obtained by replicated N-times a minimal model with central charge c < 1. A fastly convergent expansion of the twist field correlation function in terms of sphere conformal blocks with central charge Nc is obtained by exploiting covering map techniques. We discuss extensive applications of the formalism to the entanglement of two disjoint intervals in CFT, in particular we propose a conformal block expansion for the partially transposed reduced density matrix. Finally, we refine the bounds on the structure constants of unitary CFTs determined previously by the genus two modular bootstrap.

Multi-charged moments of two intervals in conformal field theory

“…A = A 1 ∪ A 2 , the ground-state entanglement entropy depends on the full operator content of the CFT, encoding all the conformal data of the model [12][13][14][15]. It is important to remark that, in this situation, the entanglement entropies quantify the entanglement between A and B but not between the two parts of A, for which one must resort to other entanglement measures such as negativity [16][17][18][19][20][21][22]. Nevertheless, from the entanglement entropies, it is possible to construct the following quantity, dubbed mutual information,…”

“…which is a measure of the total correlations between A 1 and A 2 . The computation of twointerval Rényi entanglement entropies is a difficult problem, even for minimal CFTs [21,23], as it boils down in general to determine the partition function of the theory on a higher genus n-sheeted Riemann surface [14,15]. In fact, exact analytic expressions are only available for the free theories or special limits [13][14][15][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Quench dynamics of Rényi negativities and the quasiparticle picture

“…The Rényi negativities E n with integer n ≥ 2 can also be measured in experiments [15,17,18], but they are not entanglement monotones. The entanglement negativity and Rényi negativities have been used to characterize mixed states in various quantum systems such as in harmonic oscillator chains [43][44][45][46][47][48][49][50][51], quantum spin models [25,26,[52][53][54][55][56][57][58][59][60][61][62][63], (1+1)d conformal and integrable field theories [18,[23][24][25][26][27][64][65][66][67][68][69][70][71][72][73][74][75], out-of-equilibrium settings [15, 19-21, 29, 30, 76-81]. Crucially, while for free-boson models the Rényi negativities for arbitrary real n can be efficiently computed from the two-point correlation function [43], this is not the case for freefermio...…”

Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

“…The other key ingredients are the bulk and bulk-boundary structure constants appearing in the conformal block expansion. We note that the correspondence between conformal blocks and characters has also been employed in the recent work of [107] for the evaluation of twist correlators on manifolds without boundaries.…”