Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity

Abstract

In two recent works, we studied the symmetry resolved Rényi 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.

Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems

“…Indeed, the concepts of symmetry and symmetry-breaking are ubiquitous in Physics. In recent years there has been renewed interest in studying symmetry-breaking both in and out-of-equilibrium systems [1][2][3][4][5][6][7][8][9][10][11]. Let us consider the prototypical setup of the quantum quench [12] in which a system, here a one-dimensional one, is prepared in an initial state and let to evolve under a many-body Hamiltonian H. Let us also assume that the Hamiltonian commutes with a charge operator Q, which generates an Abelian symmetry U (1).…”

Entanglement asymmetry in the ordered phase of many-body systems: the Ising field theory

“…Our approach combines the expression of the Rényi entropies in terms of twist fields via the replica trick [20,21] and its extension in the presence of additional Aharonov-Bohm fluxes [4], which stem from the action of the group and give rise to composite (charged) twist fields [22]. A vast literature regarding Integrable Field Theories where similar fields were considered is present, and we refer the reader to [23][24][25][26][27][28][29][30] for further details. However, most of these works refer to paramagnetic phases of field theories, where a single symmetric vacuum is present: there, different ways of inserting the same total Aharonov-Bohm flux among the replicas give rise to the same results (see e.g [23][24][25]).…”