Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy

By J. Cardy, O. Castro-Alvaredo, B. Doyon. 2007

336 citations recorded by the source corpus.

Abstract In this paper we compute the leading correction to the bipartite entanglement entropy at large sub-system size, in integrable quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle spectrum of the theory and not on the details of the scattering matrix. We employ the “replica trick” whereby the entropy is obtained as the derivative with respect to n of the trace of the nth power of the reduced density matrix of the sub-system, evaluated at n=1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are naturally related to branch points in an n-sheeted Riemann surface. Their two-point function directly gives the scaling limit of the trace of the nth power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this two-point function in terms of form factors of the twist fields, in order to evaluate it at large distances in the two-particle approximation. Although this is a well-known technique, the new geometry of the problem implies a modification of the form factor equations satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide solutions, which we specialize both to the Ising and sinh-Gordon models.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5f305b2d0f84143a9f76fc88c0c9eb81c16bb252

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Citations in the corpus

Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “As already mentioned, in a CFT these partition functions may be viewed as correlators of twist operators T evaluated in the product of the CFTs on each component [48, 55], i.”
Symmetry resolved entanglement in free fermionic systems (2019, background): “In this way one can further reformulate the problem in terms of a correlation function of twist fields [14].”
Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions (2021, methodology): “(G9) for Hermitian systems has been derived in several previous works [75, 80, 92].”
Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (2015, methodology): “The main advantage is that the former can be tackled with a (somehow) conventional integrable bootstrap, reminiscent of the one employed when studying correlators in integrable models [28], or branch-point twist fields [29].”
Finite temperature entanglement negativity in conformal field theory (2014, background): “The partition function on the n-sheeted surface can be casted in the form of correlation functions on the complex plane of particular operators termed branch-point twist fields [3, 39, 5].”
Entanglement entropy of two disjoint intervals in conformal field theory (2009, background): “Hence the expression (17) does indeed define local fields at (u1, 0) and (v1, 0) in the multi-copy model [17].”
Entanglement entropy of two disjoint blocks in XY chains (2010, background): “It would be interesting to explore this issue with the continuum theory in the form factor approach [32].”
Entanglement negativity in extended systems: a field theoretical approach (2012, methodology): “However, the definition of the negativity is more appealing because it is independent of basis and so calculable by quantum field theory (QFT), which naturally unveils universal features, in particular close to a quantum critical point.”
Entanglement entropy and conformal field theory (2009, background): “The twist fields defined by (12), which have been called branch-point twist fields [12], are twist fields associated with the two opposite cyclic permutation symmetries i → i + 1 and i + 1 → i (i = 1, .”
Unusual corrections to scaling in entanglement entropy (2010, background): “[4, 5, 24], for a one-dimensional quantum system on a lattice L the expression Tr ρA is given by the ratio Zn/Z n 1 , where Zn is the partition function defined by the path integral on n copies of L ⊗ imaginary time τ ∈ {−∞,+∞}, sewn together along τ = 0 so that in the interval B ⊂ L the jth sheet w”
Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases (2016, methodology): “This holds because the twist fields needed to compute the entropy are spinless [27].”