Linked cluster series expansions for twoparticle bound states
Abstract
We develop strongcoupling series expansion methods to study twoparticle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the twoparticle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the twoparticle subspace are characterized by identical quantum numbers. We discuss the solution of the twoparticle Schrödinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the lowlying excitation spectra of the models at hand, including all twoparticle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the (1+1)dimensional transverse Ising model and the twoleg spin12 Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the twoparticle continuum.
 Publication:

Physical Review B
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevB.63.144410
 arXiv:
 arXiv:condmat/0010354
 Bibcode:
 2001PhRvB..63n4410Z
 Keywords:

 75.10.b;
 75.40.Gb;
 General theory and models of magnetic ordering;
 Dynamic properties;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 10 figures, revtex