Entanglement content of quantum particle excitations. Part I. Free field theory

Abstract

We evaluate the entanglement entropy of a single connected region in excited states of onedimensional 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.

Entanglement content of quantum particle excitations. III. Graph partition functions

“…In excited states formed of a finite number of quasiparticle excitations, in the limit where the system's and regions' volumes are large, the increment of Rényi entanglement entropies due to the quasiparticles equates the entanglement entropy of certain "quasiparticle qubit states", where qubits associated to the interior and exterior of the entanglement regions represent the presence or not of quasiparticles there, and amplitudes, their uniform distribution in space. This was proven [31] for connected entanglement regions in the one-dimensional relativistic massive free boson and in the free Majorana fermion, using the form factor expansions of branch-point twist fields developed in [14] and the finite-volume form factor theory developed in [33,34]. It was also numerically verified in higher dimensions and shown in certain states of interacting models [30].…”

Entanglement content of quantum particle excitations. Part II. Disconnected regions and logarithmic negativity

“…r 1 " x 1 L " 1 L and g n p prq " 1´r`re 2πi p n , (4. 38) the function that already played an important role in the computation of the entanglement entropies of one interval [33]. The same consideration is valid for theβ rapidities.m θ,1{2 denotes the number of first order poles resulting from the third/fourth form factor having a singularity, andm θ,d denotes the number of second order poles.…”

“…This provides a formal derivation, from QFT methods, of the results presented in the previous sections, which were argued for based on the qubit picture. We follow the same strategy as for the computation presented in [33], generalized to the study of the four-point functions entering the definitions (1.10) and (1.11). All the techniques that we use in this section (branch point twist fields, finite volume form factors, doubling trick) have been exhaustively reviewed in [33] and we refer the reader to this paper for further details.…”

Front dynamics in the XY chain after local excitations

“…For the correlations we derive a relation which holds also for finite times if the separation of the spins is much larger than the correlation length. On the other hand, for the entropy we propose an ansatz that is motivated by recent results for single-mode quasiparticle excitations in a free massive quantum field theory (QFT) [26,27]. Our ansatz works perfectly in the hydrodynamic regime, thereby creating an exact relation between the magnetization and entanglement profiles.…”