Wave Functions in Two Dimensions

C. L. Kane, Steven Allan Kivelson, D. H. Lee +1 more

We construct a class of interacting-boson Hamiltonians whose exact ground-state wave functions are of Jastrow form. These Hamiltonians generally have both two- and three-body interactions; however, we show that the three-body interaction does not affect the long-wavelength physics. This enables us to deduce that (a) for Coulomb interacting bosons at T=0 the lower critical dimension is ${\mathit{d}}_{\mathit{c}}$=2; (b) in two dimensions, the ground-state wave function has the form of the modulus of the Laughlin wave function and exhibits algebraic long-range order; and (c) for short-range repulsions, we obtain a simple expression for the sound velocity. We also show that the Laughlin wave function is the generic ground-state wave function for fermions in a magnetic field corresponding to a filling factor of \ensuremath{\nu}=1/q.

Rhett J. Allain

G. F. Delll’Antonio

Abstract We prove that in two dimensions the contact interaction of two wave functions is represented by a self-adjoint operator. Together with a confining potential, this provides a stable condensate of two-particle systems. Recall that in three dimensions one has a condensate of four wave functions in contact interaction (the Bose–Einstein condensate).

W. Graham Richards

Michele Ruggeri, Saverio Moroni, Markus Holzmann

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.

Marlina Slamet, Xiao‐Yin Pan, Viraht Sahni