Symmetry Resolved Entanglement of Excited States in Quantum Field Theory
III: Bosonic and Fermionic Negativity
- URL: http://arxiv.org/abs/2302.02666v1
- Date: Mon, 6 Feb 2023 10:05:58 GMT
- Title: Symmetry Resolved Entanglement of Excited States in Quantum Field Theory
III: Bosonic and Fermionic Negativity
- Authors: Luca Capizzi, Michele Mazzoni, and Olalla A. Castro-Alvaredo
- Abstract summary: We study the resolved R'enyi entropies of quasi-particle excited states in quantum field theory.
We compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators.
We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In two recent works, we studied the symmetry resolved R\'enyi entropies of
quasi-particle excited states in quantum field theory. We found that the
entropies display many model-independent features which we discussed and
analytically characterised. In this paper we extend this line of investigation
by providing analytical and numerical evidence that a similar universal
behavior arises for the symmetry resolved negativity. In particular, we compute
the ratio of charged moments of the partially transposed reduced density matrix
as an expectation value of twist operators. These are ``fused" versions of the
more traditionally used branch point twist fields and were introduced in a
previous work. The use of twist operators allows us to perform the computation
in an arbitrary number of spacial dimensions. We show that, in the large-volume
limit, only the commutation relations between the twist operators and local
fields matter, and computations reduce to a purely combinatorial problem. We
address some specific issues regarding fermionic excitations, whose treatment
requires the notion of partial time-reversal transformation, and we discuss the
differences and analogies with their bosonic counterpart. We find that although
the operation of partial transposition requires a redefinition for fermionic
theories, the ratio of the negativity moments between an excited state and the
ground state is universal and identical for fermions and bosons as well as for
a large variety of very different states, ranging from simple qubit states to
the excited states of free quantum field theories. Our predictions are tested
numerically on a 1D Fermi chain.
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