The nearest-neighbor resonating-valence bond state in a Grassmannian form
The nearest-neighbor resonating-valence bond (NNRVB) state is studied using classical anticommuting (Grassmann) variables. The classical partition function corresponding to the self-overlap of the NNRVB wavefunction is generated from a local (bond) Hamiltonian expressed in terms of four anticommuting variables. It is shown that the one-particle-per-site constraint introduces an interaction term which is a local product of all four variables. Two approaches are applied to study this Hamiltonian: (i) a self-consistent field decoupling scheme and (ii) a systematic perturbation expansion around the unconstrained soluble point. Bounds on the norm of the wavefunction are derived. Extensions to the presence of holes, long-range valence bonds, and the introduction of phase fluctuations [which violate the Marshall sign rule and yield aU(1) gauge theory] are discussed.

title: GRASSMANNIAN APPROACH TO THE RESONATING-VALENCE-BOND STATE OF THE 2D HEISENBERG ANTIFERROMAGNET
abstract: A systematic representation of the resonating-valence-bond state of the 2D spin-1/2 Heisenberg antiferromagnet in terms of anticommuting Grassmann variables is derived. This representation is extended to the dilute case and the holon statistics are considered. Independent phase fluctuations on each valence-bond yield a U(1) gauge theory with low-lying gapless excitations in accordance with other approaches.

title: Flux-carrying fermions and the second virial coefficient.
abstract: The second virial coefficient {ital B}{sub 2} for a system of spin-one-half flux-carrying fermions is computed. It is found that there arise significant differences from known results for the corresponding spinless system. Apart from the existence of cusps and a restricted periodicity of {ital B}{sub 2} when viewed as a function of the flux parameter {alpha}, one obtains here the remarkable result that there exist discontinuities in {ital B}{sub 2} at all even, nonzero values of {alpha}.

title: Initial nucleon structure results with chiral quarks at the physical point
abstract: S. Syritsyn∗ a, T. Blum a,b, M. Engelhardt c, J. Green d , T. Izubuchi a, C. Jung a, S. Krieg e, M. Lin f , S. Meinel a,g, J. Negele h, S. Ohta i, j,a, A. Pochinsky h, E. Shintani a,k (RBC and LHP collaborations) a RIKEN/BNL Research Center, Brookhaven National Laboratory, Upton, NY, 11973, USA b Physics Department, University of Connecticut, Storrs, CT 06269, USA c Department of Physics, New Mexico State University, Las Cruces, NM 88003, USA d Institut fur Kernphysik, Johannes Gutenberg-Universitat Mainz, D-55099 Mainz, Germany e Bergische Universitat Wuppertal, D-42119 Wuppertal, Germany and IAS, Julich Supercomputing Centre, Forschungszentrum Julich, D-52425 Julich, Germany f Computational Science Center, Brookhaven National Laboratory, Upton, NY 11973, USA g Department of Physics, University of Arizona, Tucson, AZ 85721, USA h Massachusetts Institute of Technology, Cambridge, MA 02139, USA i Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki 3050801, Japan j Department of Particle and Nuclear Physics, SOKENDAI, Hayama, Kanagawa, 2400193, Japan k PRISMA Cluster of Excellence, Institut fur Kernphysik and Helmholtz Institute Mainz, Johannes Gutenberg-Universitat Mainz, D-55099 Mainz, Germany E-mail: ssyritsyn@quark.phy.bnl.gov