Universal entanglement and correlation measure in two-dimensional conformal field theories

Abstract

We calculate the amount of entanglement shared by two intervals in the ground state of a (1+1)-dimensional conformal field theory (CFT), quantified by an entanglement measure $\mathcal{E}$ based on the computable cross norm (CCNR) criterion. Unlike negativity or mutual information, we show that $\mathcal{E}$ has a universal expression even for two disjoint intervals, which depends only on the geometry, the central charge c, and the thermal partition function of the CFT. We prove this universal expression in the replica approach, where the Riemann surface for calculating $\mathcal{E}$ at each order n is always a torus topologically. By analytic continuation, result of n=1/2 gives the value of $\mathcal{E}$. Furthermore, the results of other values of n also yield meaningful conclusions: The n=1 result gives a general formula for the two-interval purity, which enables us to calculate the Renyi-2 N-partite information for N<=4 intervals; while the $n=\infty$ result bounds the correlation function of the two intervals. We verify our findings numerically in the spin-1/2 XXZ chain, whose ground state is described by the Luttinger liquid.

5+2 pages, 3+2 figures; published version

References in corpus (15)

• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement of low-energy excitations in Conformal Field Theory
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Universality of corner entanglement in conformal field theories
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement Entropy and Twist Fields
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Entanglement barrier and its symmetry resolution: theory and experiment
• Universal tripartite entanglement in one-dimensional many-body systems
• Multi-charged moments of two intervals in conformal field theory
• Reflected entropy in random tensor networks II: a topological index from the canonical purification

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• More on symmetry resolved operator entanglement
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain