2000/10/23 by Weihong Zheng, C. J. Hamer, R. R. P. Singh +4 · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.63.144410
published as Phys. Rev. B 63, 144410 (2001) · 10 figures, revtex
arxiv created 2000/10/23 · openalex publication_date 2001/03/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle 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 two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schr"odinger 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 low-lying excitation spectra of the models at hand, including all two-particle 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 two-leg spin\ensuremath-(1)/(2) Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.