Coordinate representation of the two-spinon wave function and spinon interaction in the Haldane-Shastry model

Abstract

By deriving and studying the coordinate representation for the two-spinon wavefunction, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a shortrange attraction and causes a resonant enhancement in the two-spinon wavefunction at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the resonant enhancement, given by the two-spinon wavefunction at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.

Coloron excitations of the SU(3) Haldane-Shastry model

“…The first term in the resulting expression can be treated in analogy to the two-spinon states in the SU͑2͒ HSM. 35 Specifically, we find…”

Many-Spinon States and the Secret Significance of Young Tableaux

“…At present, only very few of these matrix elements are known, and the exact expressions for these elements for finite chains appear rather complicated [19][20][21]. These expressions, however, greatly simplify in the thermodynamic limit, and there is hope that a method to obtain them directly in this limit can be developed.…”

Non-Abelian fractional Chern insulator in disk geometry

“…However, expanding the Moore-Read state with more than 4 particles is very difficult. Fortunately, the Jacks provide an effective way to decompose Moore-Read state into symmetric monomials (for bosons) or anti-symmetric Slater determinants (for fermions) [17][18][19][20], i.e. the non-normalized Ψ MR ({z i }) = k c k Ψ J k ({z i }).…”

“…Fortunately, trial WF of Moore-Read state with a simple analytic expression has been proposed from a conformal field theory perspective [2]. Similar to the Laughlin WFs, the Moore-Read state can be decomposed into anti-symmetric Slater determinants (for fermions) or symmetric monomials (for bosons) with the help of the Jack symmetric polynomials (Jacks) [17][18][19][20], which naturally reflects the generalized Pauli principle (GPP) [21][22][23][24] in the Fock space. The GPP and the Jacks have been extended [25,26] to the lattice analogs of FQH states in the absence of external magnetic field, which are named fractional Chern insulaors (FCIs) .…”

“…S1 with finite number of bosons). Similar to the Laughlin states, this bosonic Moore-Read state can be decompose into symmetric monomials (the Jacks basis) based on the Jacks [17][18][19][20]…”