Abstract
We evaluate the entanglement entropy of a single connected region in excited states of one-dimensional massive free theories with finite numbers of particles, in the limit of large volume and region length. For this purpose, we use finite-volume form factor expansions of branch-point twist field two-point functions. We find that the additive contribution to the entanglement due to the presence of particles has a simple “qubit” interpretation, and is largely independent of momenta: it only depends on the numbers of groups of particles with equal momenta. We conjecture that at large momenta, the same result holds for any volume and region lengths, including at small scales. We provide accurate numerical verifications.
Highlights
Measures of entanglement, such as the entanglement entropy, have attracted much attention in recent years, in the context of one-dimensional many body quantum systems
Of excited states with finite energy density in quantum field theory (QFT) or quantum lattice models is very simple by the eigenstate thermalization hypothesis: it is dominated by the thermodynamic entropy of the corresponding
The computation of the ratio (1.9) for a generic k-particle excited state of a massive free theory in finite volume involves the use of a considerable number of techniques we will be presenting : the form factor programme for branch point twist fields [24], the generalization of this programme for finite volume correlators following the ideas of [33, 34], the rewriting of the branch point twist field in terms of U(1) fields of the replica free theory by employing the “doubling trick” introduced in [35]
Summary
Measures of entanglement, such as the entanglement entropy, have attracted much attention in recent years, in the context of one-dimensional many body quantum systems (see e.g. review articles in [1,2,3]). The EE of excited states with finite energy density in quantum field theory (QFT) or quantum lattice models is very simple by the eigenstate thermalization hypothesis (or its extension to integrable systems): it is dominated by the thermodynamic entropy of the corresponding. Employing the branch point twist field approach [24], we compute the difference between the Renyi entropy in the excited state and in the ground state, in this limit, lim. We highlight the challenges of generalizing such connection to finite volume and excited states We explain how these challenges may be resolved in the case of the massive free boson theory and introduce the “doubling trick” in this context. In appendix C we prove some properties of the functions gpn(r) in terms of which all EEs can be expressed
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