Multi-charged moments of two intervals in conformal field theory

Abstract

We study the multi-charged moments for two disjoint intervals in the ground state of two 1 + 1 dimensional CFTs with central charge c = 1 and global U(1) symmetry: the massless Dirac field theory and the compact boson (Luttinger liquid). For this purpose, we compute the partition function on the higher genus Riemann surface arising from the replica method in the presence of background magnetic fluxes between the sheets of the surface. We consider the general situation in which the fluxes generate different twisted boundary conditions at each branch point. The obtained multi-charged moments allow us to derive the symmetry resolution of the Rényi entanglement entropies and the mutual information for non complementary bipartitions. We check our findings against exact numerical results for the tight-binding model, which is a lattice realisation of the massless Dirac theory.

Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case

“…These expressions are however simplified to algebraic functions of interval lengths and distances using the conjectures made in eq.(4.36)-(4.39). Similar conjectures were first made in [36] for the two disjoint intervals case. The symmetry resolved Rényi entropy was then obtained by evaluating the Fourier transform of the charged moments.…”

“…The multi-charged moments of free compact boson in two disjoint intervals case for Rényi entropy was first obtained in [36], these moments were then used to study the symmetry resolved Rényi entropy and mutual information. In [52], these quantities were obtained for Rényi negativity to study the symmetry-resolved Rényi negativity in the same settings.…”

“…(4.5) ill-defined. This issue is resolved by introducing the regularised vertex operators V ( * ) [36]. The normalised holomorphic differentials ν j,r (z i ) exhibit the leading order singular behaviour as…”

“…In the rest of this section, we will evaluate this correlation function for arbitrary values of N and n. We first revisit the two disjoint intervals case, we will use a different canonical homology basis than [36]. We then extend these results to N > 2.…”

Symmetry-resolved entanglement in critical non-Hermitian systems

“…The basic tool to investigate how entanglement distributes among symmetry sectors is the symmetry-resolved entanglement entropy [35][36][37], which provides a finer measure of the entanglement content in extended systems that is not accessible from the total entanglement entropy. This fact has currently triggered an intense research activity on the interplay between symmetries and entanglement in very different systems, including spin chains [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], integrable [53][54][55][56][57][58][59][60][61] and conformal field theories [36,37,[62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77], and involving diverse contexts su...…”