Universal R\'enyi Entropy of Quasiparticle Excitations
- URL: http://arxiv.org/abs/2010.13973v3
- Date: Wed, 10 Nov 2021 12:40:00 GMT
- Title: Universal R\'enyi Entropy of Quasiparticle Excitations
- Authors: Jiaju Zhang, M. A. Rajabpour
- Abstract summary: We calculate R'enyi entropies of quasiparticle excitations in the many-body gapped fermions, bosons, and XY chains.
We find additional contributions to the universal R'enyi entropy in the excited states with quasiparticles of different momenta.
- Score: 0.24366811507669117
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The R\'enyi entropies of quasiparticle excitations in the many-body gapped
systems show a remarkable universal picture which can be understood partially
by combination of a semiclassical argument with the quantum effect of
(in)distinguishability. The universal R\'enyi entropies are independent of the
model, the quasiparticle momenta, and the connectedness of the subsystem. In
this letter we calculate exactly the single-interval and double-interval
R\'enyi entropies of quasiparticle excitations in the many-body gapped
fermions, bosons, and XY chains. We find additional contributions to the
universal R\'enyi entropy in the excited states with quasiparticles of
different momenta. The additional terms are different in the fermionic and
bosonic chains, depend on the momentum differences of the quasiparticles, and
are different for the single interval and the double interval. We derive the
analytical R\'enyi entropy in the extremely gapped limit, matching perfectly
the numerical results as long as either the intrinsic correlation length of the
model or all the de Broglie wavelengths of the quasiparticles are small. When
the momentum difference of any pair of distinct quasiparticles is small, the
additional terms are non-negligible. On the contrary, when the difference of
the momenta of each pair of distinct quasiparticles is large, the additional
terms could be neglected. The universal single-interval R\'enyi entropy and its
additional terms in the XY chain are the same as those in the fermionic chain,
while the universal R\'enyi entropy of the double intervals and its additional
terms are different, due to the fact that the local degrees of freedom of the
XY chain are the Pauli matrices not the spinless fermions. We argue that the
derived formulas have universal properties and can be applied for a wider range
of models than those discussed here.
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