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...

For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.

We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d − 1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1)ν > 2 rather than the usual Harris criterion dν > 2, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. Puzzling results have been reported, however, on phase transitions in topologically disordered systems, i.e., systems on lattices with random connectivity. For example, the Ising magnet on a three-dimensional (3D) random Voronoi lattice displays the same critical behavior as the Ising model on a cubic lattice [7,8] even though Harris' inequality is violated. An analogous violation was found for the 3-state Potts model on a 2D random Voronoi lattice [9]. The regular 2D 8-state Potts model features a first-order phase transition. In contrast to the prediction of the Imry-Ma criterion, the transition remains of first order on a random Voronoi lattice [10].The nonequilibrium transition of the contact process features an even more striking discrepancy. This system violates Harris' inequality [11]. Disorder introduced via dilution or random transition rates results in an infiniterandomness critical point and strong Griffiths singularities [12,13]. In contrast, the contact process on a 2D random Voronoi lattice shows clean critical behavior and no trace of the exotic strong-randomness physics [14].To explain the unexpected failures of the Harris and Imry-Ma criteria, several authors suggested that, perhaps, the existing results are not in the asymptotic regime. Thus, much larger systems would be necessary to observe the true asymptotic behavior which, presumably, agrees with the Harris and Imry-Ma criteria. However, given the large systems employed in some of the cited work, this would imply enormous crossover lengths which do not appear likely because the coordination number fluctuations of the Voronoi lattice are not particularly small [15]. What, then, causes the failure of the Harris and Imry-Ma criteria on random Voronoi lattices?In this Letter, we show that 2D random Voronoi lattices belong to a broad class of random lattices whose disorder fluctuations feature strong anticorrelations and thus decay qualitatively faster with increasing length scale than those of generic random systems. This class comprises lattices whose total coordination (total number of bonds) does not fluctuate. Such lattices are particularly prevalent in 2D because the Euler e...

We study nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such "random-field" disorder is known to have dramatic effects: It prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we show that the phase transition of the one-dimensional generalized contact process persists in the presence of random field disorder. The ultraslow dynamics in the symmetry-broken phase is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by large-scale Monte-Carlo simulations.