Entanglement Content of Quasiparticle Excitations

Abstract

We investigate the quantum entanglement content of quasi-particle excitations in extended manybody systems. We show that such excitations give an additive contribution to the bi-partite von Neumann and Rényi entanglement entropies that takes a simple, universal form. It is largely independent of the momenta and masses of the excitations, and of the geometry, dimension and connectedness of the entanglement region. The result has a natural quantum information theoretic interpretation as the entanglement of a state where each quasi-particle is associated with two qubits representing their presence within and without the entanglement region, taking into account quantum (in)distinguishability. This applies to any excited state composed of finite numbers of quasi-particles with finite De Broglie wavelengths or finite intrinsic correlation length. We derive this result analytically in one-dimensional massive bosonic and fermionic free field theories and for simple setups in higher dimensions. We provide numerical evidence for the harmonic chain and the two-dimensional harmonic lattice in all regimes where excitations have quasi-particle properties. Finally, we provide supporting calculations for integrable spin chain models and other situations without particle production. Our results point to new possibilities for creating entangled states using many-body quantum systems. arXiv:1805.04948v1 [cond-mat.stat-mech]

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

“…S 2 n pr 1 , r 3 q " logpr 2n`p 1´rq 2n`p 2rp1´rqq n q 1´n , (B. 7) and this is the expected formula found in [32,33]. The matrix ρ T B…”

“…As explained in [32], the analytical predictions are expected to be valid in the "quasiparticle regime", where the lengths of all connected regions (the regions A and B, and the connected components of C) are large as compared to either the correlation length m´1, or the De Broglie wavelengths 2π p of all excitations (where p is the momentum). Below, all momenta are chosen to be well within the QFT regime.…”

“…In two recent works [32,33] we have investi- gated the entanglement entropy of gapped systems in zero-density excited states, where excitations have a (quasi-)particle interpretation. We found a very intuitive mathematical structure for the entropy differences between the ground state and such excited states.…”

Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems

“…Since the F Υ,n (A) is function only of x for all excitations, the additional term in the entanglement entropies is always of order 1 in L, showing that the universal logarithmic behaviour for the ground-state persists for all low-lying excited states in CFT. Higher excited states, in the middle of the spectrum of microscopical models, have instead generically extensive entanglement entropy [23,[55][56][57][58][59][60][61][62][63][64] (see [65] for low-lying excitations in massive field theories). For the case of OBC, which is of major interest here, we consider a systems of length 2L, i.e.…”

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

“…For further results on the entanglement entropy of the low-lying excited states in CFTs see [48][49][50][51][52][53][54]. Recently, there has also been analytical calculations regarding the quantum entanglement content of the quasi-particle excitations in massive field theories and integrable chains [55,56].…”