Two-Point Functions of Composite Twist Fields in the Ising Field Theory

Abstract

All standard measures of bipartite entanglement in one-dimensional quantum field theories can be expressed in terms of correlators of branch point twist fields, here denoted by $\mathcal{T}$ and ${\mathcal{T}}^{†}$. These are symmetry fields associated to cyclic permutation symmetry in a replica theory and having the smallest conformal dimension at the critical point. Recently, other twist fields (composite twist fields), typically of higher dimension, have been shown to play a role in the study of a new measure of entanglement known as the symmetry resolved entanglement entropy. In this paper we give an exact expression for the two-point function of a composite twist field that arises in the Ising field theory. In doing so we extend the techniques originally developed for the standard branch point twist field in free theories as well as an existing computation due to Horváth and Calabrese of the same two-point function which focused on the leading large-distance contribution. We study the ground state two-point function of the composite twist field ${\mathcal{T}}_{\mu }$ and its conjugate ${\mathcal{T}}_{\mu }^{†}$. At criticality, this field can be defined as the leading field in the operator product expansion of $\mathcal{T}$ and the disorder field $\mu$. We find a general formula for $\log ⟨{\mathcal{T}}_{\mu }(0){\mathcal{T}}_{\mu }^{†}(r)⟩$ and for (the derivative of) its analytic continuation to positive real replica numbers greater than 1. We check our formula for consistency by showing that at short distances it exactly reproduces the expected conformal dimension

25 pages and 3 figures

References in corpus (12)

• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Entanglement equipartition in critical random spin chains
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Charged Moments in $W_3$ Higher Spin Holography
• Bi-partite entanglement entropy in integrable models with backscattering
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

Cited by in corpus (11)

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• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Symmetry-resolved entanglement in fermionic systems with dissipation
• Charge-resolved entanglement in the presence of topological defects
• Symmetry Resolution in non-Lorentzian Field Theories
• Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Entanglement content of kink excitations
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach
• Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench