We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.

Symmetry decomposition of negativity of massless free fermions / Murciano, Sara; Bonsignori, Riccarda; Calabrese, Pasquale. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 10:5(2021), pp. 1-45. [10.21468/SCIPOSTPHYS.10.5.111]

Symmetry decomposition of negativity of massless free fermions

Sara Murciano
;
Riccarda Bonsignori
;
Pasquale Calabrese
2021-01-01

Abstract

We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.
10
5
1
45
111
10.21468/SCIPOSTPHYS.10.5.111
https://arxiv.org/abs/2102.10054
Murciano, Sara; Bonsignori, Riccarda; Calabrese, Pasquale
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/124970
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 28
social impact