An explicit construction of wave functions

S. Viefers, Emil J. Bergholtz, T. H. Hansson +2 more

It has long been known that Laughlin's wave functions, describing the fractional quantum Hall effect at filling fractions ν=1/(2k+1), can be obtained as correlation functions in conformal field theory. We show how to generalize this approach to construct explicit trial wave functions for all states in the quantum Hall hierarchy corresponding to quasiparticle (as opposed to quasihole) condensates, including the recently observed state at ν= 4/11. At the filling fractions ν= n/(2np+1) this construction exactly reproduces Jain's composite fermion wave functions. An explicit connection is made to Wen's topological classification of FQH states.

Marlina Slamet, Xiao‐Yin Pan, Viraht Sahni

Jiarui Jiao, Chao Xu, Congjun Wu +1 more

Although BCS wave functions for superconductors under periodic boundary conditions are well established, obtaining an explicit form of the many-body BCS wave function under open boundary condition is usually a nontrivial problem. In this work, we construct the exact BCS ground-state wave function of a one-dimensional spin-$\frac12$ superconductor with $p+is$ pairing symmetry under open boundary conditions for special sets of parameters. The spin magnetization on the edges is calculated explicitly using the obtained wave function. Our work is useful for obtaining deeper understandings of open $p+ is$ superconducting chains on a wave-function level.

Arkady Bolotin

K. T. Hecht

Ronny Thomale, Dirk Schuricht, Martin Greiter

We construct the explicit two-holon eigenstates of the SU(2) Kuramoto-Yokoyama model at the level of explicit wave functions. We derive the exact energies and obtain the individual holon momenta, which are quantized according to the half-Fermi statistics of the holons.