Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to 10 5 particles.Entanglement encodes the amount of non-classical information shared between complementary parts of an extended quantum state. For a pure state described by density matrix ρ, it can be quantified via the Rényi entanglement entropies: S α (ρ A ) = (1 − α) −1 ln Tr ρ α A where ρ A is the reduced density matrix of subsystem A and S α is a non-increasing function of α. While evaluation of the α = 1 (von Neumann) entanglement entropy requires a complete reconstruction of ρ, [1,2], integer values with α > 1 can be represented as the expectation value of a local operator [3]. This has enabled entanglement measurements in a wide variety of many-body states, both via quantum Monte Carlo [4-8] and experimental quantum simulators employing ultra-cold atoms [9][10][11][12][13][14]. In these systems, conservation of total particle number N may restrict the set of possible local operations, (a superselection rule) and can potentially limit the amount of entanglement that can be physically accessed [15][16][17][18][19][20][21][22]. For example, while a superfluid of N bosonic 87 Rb atoms in a one-dimensional optical lattice is highly entangled under a bipartition into spatial subregions [10], much of the entanglement is generated by particle fluctuations that cannot be transferred to a quantum register without access to a global phase reference [23]. Wiseman and Vaccaro introduced an operational measure of entropy to quantify these effects [17], but it is limited to the special case of α = 1 and thus cannot be used in tandem with current simulation and experimental studies of entanglement.In this paper, we study how the operational entanglement can be generalized to the Rényi entropies with α = 1. Recalling its definition for α = 1, it is constructed by averaging the contributions to S 1 coming from each physical number of particles in the subsystem:where ρ An = P An ρ A P An /P n is the projection into the sector of n particles in A, A n , via P An which occurs with probability P n = Tr P An ρ A P An . This projection constitutes a local operation which can only decrease entanglemen...

Recent elastic and inelastic neutron scattering studies of the highly frustrated pyrochlore antiferromagnet Tb 2 Ti 2 O 7 have shown some very intriguing features that cannot be modeled by the local ͗111͘ classical Ising model, naively expected to describe this system at low temperatures. By including single-ion excitations from the ground state doublet to higher crystal field levels, we successfully describe the elastic neutron scattering pattern and dispersion relations in Tb 2 Ti 2 O 7 , quantitatively consistent with experimental observations.

The magnetic pyrochlore oxide materials of general chemical formula R 2 Ti 2 O 7 and R 2 Sn 2 O 7 (R ≡ rare earth) display a host of interesting physical behaviours depending on the flavour of rare earth ion. These properties depend on the value of the total magnetic moment, the crystal field interactions at each rare earth site and the complex interplay between magnetic exchange and longrange dipole-dipole interactions. This work focuses on the low temperature physics of the dipolar isotropic frustrated antiferromagnetic pyrochlore materials. Candidate magnetic ground states are numerically determined at zero temperature and the role of quantum spin fluctuations around these states are studied using a Holstein-Primakoff spin wave expansion to order 1/S. The results indicate the strong stability of the proposed classical ground states against quantum fluctuations. The inclusion of long range dipole interactions causes a restoration of symmetry and a suppression of the observed anisotropy gap leading to an increase in quantum fluctuations in the ground state when compared to a model with truncated dipole interactions. The system retains most of its classical character and there is little deviation from the fully ordered moment at zero temperature.