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arXiv:2210.06743 · Journal of High Energy Physics

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

Himanshu Gaur, Urjit A. Yajnik

Published Feb 13, 2023• 14 citations
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Abstract

Abstract In this paper, we study the symmetry decomposition of Rényi negativity into charge imbalance sectors for the 1+1 dimensional free compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals. We obtain multicharged and charged Rényi negativity moments by computing the four-point correlator of flux-generating vertex operators on the Riemann surface. We then obtain charge imbalance resolved Rényi negativity by taking the Fourier transform of the charged moments. Finally, we match our results against the tight-binding model as a numerical check.

DOI
10.1007/jhep02(2023)118

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Abstract In this paper, we study the symmetry decomposition of Rényi negativity into charge imbalance sectors for the 1+1 dimensional free compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals. We obtain multicharged and charged Rényi negativity moments by computing the four-point correlator of flux-generating vertex operators on the Riemann surface. We then obtain charge imbalance resolved Rényi negativity by taking the Fourier transform of the charged moments. Finally, we match our results against the tight-binding model as a numerical check.
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Abstract 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.
In this paper, we consider the computation of symmetry resolved entanglement entropy of two disjoint intervals in the 1+11+11+1 dimensional free compactified boson conformal field theory 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 charge imbalance resolved R\'enyi negativity. We test our analytic formula against exact numerical computation in the complex harmonic chain, finding perfect agreements.
A bstract We investigate mixed-state bipartite entanglement between multiple disjoint intervals using the computable cross-norm criterion (CCNR). We consider entanglement between a single interval and the union of remaining disjoint intervals, and compute 2-Rényi CCNR negativity for a 2d massless compact boson. The expression for 2-Rényi CCNR negativity is given in terms of cross-ratios and Riemann period matrices of Riemann surfaces involved in the calculation. In general, the Riemann surfaces involved in the calculation of n -Rényi CCNR negativity do not possess a Z n symmetry. We also evaluate the reflected Rényi entropy related to the 2-Rényi CCNR negativity. This reflected Rényi entropy is a universal quantity. We extend these calculations to the 2d massless Dirac fermions as well. Finally, the analytical results are checked against the numerical evaluations in the tight-binding model and are found to be in good agreement.
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