The nonlocal properties of the W states are investigated under particle loss. By removing all but two particles from an N -qubit W state, the resulting two-qubit state is still entangled. Hence, the W state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality introduced in [Phys. Rev. A 86, 042113]. Namely, we inquire what is the minimal number of particles that must be removed from the W state so that the resulting state becomes local. We bound this value in function of N qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between 2N/5 and N/2 for large N . We also develop a framework to establish bounds for more than two settings per site.

International audienceUsing a positive semidefinite operator technique one deduces exact ground states for a zig-zag hexagon chain described by a non-integrable Hubbard model with on-site repulsion. Flat bands are not present in the bare band structure, and the operators $\hat B^{\dagger}_{\mu,\sigma}$ introducing the electrons into the ground state, are all extended operators and confined in the quasi 1D chain structure of the system. Consequently, increasing the number of carriers, the $\hat B^{\dagger}_{\mu,\sigma}$ operators become connected i.e. touch each other on several lattice sites. Hence the spin projection of the carriers becomes correlated in order to minimize the ground state energy by reducing as much as possible the double occupancy leading to a ferromagnetic ground state. This result demonstrates in exact terms in a many-body frame that the conjecture made at two-particle level by G. Brocks et al. [Phys.Rev.Lett. {\bf 93},146405, (2004)] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes is clearly viable, and opens new directions in the search for routes in obtaining organic ferromagnetism. Due to the itinerant nature of the obtained ferromagnetic ground state, the systems under discussion may have also direct applicatio

Abstract. Based on positive semidefinite operator properties, an exact ground state solution is deduced for a 2D Hubbard model with periodic boundary conditions on small samples. The obtained ferromagnetic behavior is used as a possible explanation of the ferromagnetism occurring in nano-samples made of non-magnetic but metallic materials. IntroductionIt is known that if a sample is constructed from non-magnetic metal (for example Au), and the size of the object is decreased to nanoscale values, the material can become ferromagnetic [1,2]. Below we provide a possible explanation for this effect, which requires only Coulomb repulsion between itinerant carriers, closed surface and quantum mechanical effects. For this reason we analyze a two dimensional L L × square lattice at arbitrary but finite L size with periodic boundary conditions in both directions, containing itinerant electrons. The Coulomb repulsion in this many-body system is screened by the itinerant system, consequently is of short-range type, and hence is taken into account for simplicity by the on-site Coulomb repulsion alone. Below this Hubbard system is solved exactly for the ground state in a restricted region of the parameter space, obtaining a ferromagnetic solution for small L values.The solution procedure (see [3][4][5][6][7] for details) is based on positive semidefinite operator properties. The technique first transforms in exact terms the Hamiltonian Ĥ of the system in a positive semidefinite form ˆĤ P C = + where P is a positive semidefinite operator while C is

No abstract

This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.A technique based on positive semidefinite operator properties has been used in deducing exact ground states for hexagon chains of polyphenylene type (hexagons interconnected by bonds build up the 1D periodic structure), placed in a constant external magnetic field B perpendicular to the surface containing the system. The used Hubbard type of model takes into account B by Peierls phase factors, and has the peculiar property to provide only flat bands in the bare band structure for elevated external field values independent on the parameters entering in the kinetic part of the Hamiltonian. The deduced ground states are non-magnetic or ferromagnetic in character, localized in the thermodynamic limit, and besides the fact that B is able to switch the system between different phases, emphasize that the localization length and connectivity conditions can be tuned by external magnetic fields.