Some properties of a new class of variational wave functions for boson systems are studied. This study extends the Jastrow class, and many-body correlations are implicitly introduced by a coupling of the particle coordinates to subsidiary shadow variables. We prove that the new wave function has Bose-Einstein condensation both in the liquid and in the solid phase. The maximum-overlap criterion for this wave function with the exact ground state is developed. The kind of Jastrow correlations implicitly contained in the new wave function is studied and we formulate a theory of correlations based on the reference interaction site model.
Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than
SU(2). Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with
SU(3) symmetry. Using a combination of homotopy analysis and analytic field theory we identify a family of solitonic wave functions characterized by integer charge
Q=(QA,QB,QC), with
QA+QB+QC=0. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that solitons with charge $\mathbf{Q}=(1,1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)$ spontaneously decay into a pair of solitons with elementary topological charge, and emergent interactions. This result suggests that it could be possible to realize a class of interacting soliton, with no classical analog, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge group $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$.
Jastrow-Slater and correlator product state wave functions, two classes of quantum many-body wave functions, are commonly studied using Monte Carlo methods with the associated drawbacks of stochastic error. Here we show that efficient nonstochastic algorithms for these wave functions exist, both for observable evaluation and for optimization. The algorithms rely on the structure of these states as a product of local, commuting, invertible operators acting on a simple reference wave function. We describe the nonstochastic energy evaluation and optimization algorithms, and demonstrate them with applications to the Heisenberg and spinless and full Hubbard models. Our results demonstrate that the nonstochastic algorithms yield optimized wave functions and energies very close to those obtained with the variational Monte Carlo algorithm. Such algorithms provide new criteria for identifying new classes of wave functions for efficient computational simulation.