1996/10/31 by G. Sierra, Germán Sierra
Physics and Astronomy · #Diagonal #Generalization #Hamiltonian (control theory) #Modulo #Phase diagram #Physics of Superconductivity and Magnetism #Quantum many-body systems #Sigma #Spin (aerodynamics) #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1007/bfb0104637
published as Lectures Notes in Physics, vol.478, eds. G. Sierra , and M.A. Martin-Delgado, Springer-Verlag (1997). · 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are added
arxiv created 1996/11/13 · openalex publication_date 2008/04/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the θ parameter depending on the spin S, the number of legs nℓ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain θ= 0 or 2 πS depending on wether nℓ, is even or odd, while for diagonal blocks we obtain θ= 2 πS nℓ. Both results agree modulo 2 π, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with nℓ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.