On Models with Inverse-Square Exchange

A one-dimensional quantum N-body system of either fermions or bosons with $SU(n)$ colors interacting via inverse-square exchange is presented in this article. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product type wave function. The class of states we construct in this paper corresponds to the ground state and the low energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e. the charge, spin velocities, etc.), explicitly. The correlation exponent and the compressibility of are also found. As expected the general harmonic relation(i.e. $v_S=(v_Nv_J)^{1/2}$) is satisfied among the charge and spin velocities.Comment: 26 page

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Conformal Field Theory on the Fermi Surface

The Fermi surface may be usefully viewed as a collection of 1+1 dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground state properties of the Fermi gas including entanglement entropy and number fluctuations. The 1+1 dimensional picture also generalizes to finite temperature and the presence of interactions. Finally, I argue that the low energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface.Comment: 4 pages + references, 2 figure

Two quantum spin models on the checkerboard lattice with an exact two-fold degenerate Shastry-Sutherland ground state

Two quantum spin models with bilinear-biquadratic exchange interactions are constructed on the checkerboard lattice. It is proved that, under certain sufficient conditions on the exchange parameters, their ground states consist of two degenerate Shastry-Sutherland singlet configurations. The constructions are studied for arbitrary spin-S. The sufficient conditions for the existence of ferromagnetic ground state are also found exactly. The approximate quantum phase diagrams are presented using the exact results, together with a variational estimate for the N\'eel antiferromagnetic phase. A two-leg spin-1/2 ladder model, based on one of the above constructions, is considered which admits exact solution for a large number of eigenstates. The ladder model is shown to have exact level-crossing between the rung-singlet state and the AKLT state in the singlet ground state. Also introduced is the notion of perpendicularity for quantum spin vectors, which appears in the discussion on one of the two checkerboard models, and is discussed in the Appendix.Comment: Revtex, 10 pages, 6 figures, 3 table