Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

In this paper, we consider the computation of charged moments of the reduced density matrix of two disjoint intervals in the 1+1 dimensional free compactified boson conformal field theory (CFT) by studying the four-point function of the fluxed twist fields. We obtained the exact scaling function of this four-point function and discussed its decompactification limit. This scaling function was used to obtain the charged moments of the partial transpose which we refer as charged Rényi negativity. These charged moments and the charged moments of the partial transpose are essential for the problem of symmetry decomposition of the corresponding entanglement measures. We test our analytic formula against exact numerical computation in the complex harmonic chain, finding perfect agreements.

Section: Jhep02(2022)117mentioning

confidence: 99%

Charged Rényi negativity of massless free bosons

Chen

2022

“…[4]. Important examples include relative entropy [5,6], quantum computational complexity [7][8][9], tensor networks [10,11], and quantum error correction [12,13], entwinement [14], entanglement entropy at genus one [15] and entanglement measures probing the entanglement shadow [16]. All these examples treat CFTs at large central charge.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

Weisenberger

Zhao

Northe

et al. 2021

We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

Definitions of entwinement

Craps

Clerck

López

2023

Entwinement was first introduced as the CFT dual to extremal, non-minimal geodesics of quotiented AdS3 spaces. It was heuristically meant to capture the entanglement of internal, gauged degrees of freedom, for instance in the symmetric product orbifold CFT of the D1/D5 brane system. The literature now contains different, and sometimes inequivalent, field theory definitions of entwinement. In this paper, we build a discretized lattice model of symmetric product orbifold CFTs, and explicitly construct a gauge-invariant reduced density matrix whose von Neumann entropy agrees with the holographic computation of entwinement. Refining earlier notions, our construction gives meaning to the entwinement of an interval of given size within a long string of specific length. We discuss similarities and differences with previous definitions of entwinement.