paper

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J1, J2 between first and second neighbors

arXiv:1603.02108 · doi:10.1088/0953-8984/28/17/175603

Abstract

The spin-1/2 chain with isotropic exchange J1, J2 > 0 between first and second neighbors is frustrated for either sign of J1 and has a singlet ground state (GS) for J1/J2 $\geq - 4$ . Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J1/J2 are evaluated using exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations. The wave vector $q_{G}$ of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor $S (q)$ . Variable $q_{G}$ indicates IC phases in two $J 1/ J 2$ intervals, [ -4, -1.24] and [0.44, 2], and a C-IC point at J1/J2 = 2. The decoupled C phase in [-1.24, 0.44] has constant $q_{G} = I ¨ /2$ , nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, $E_{m}$ and $E_{I ¨} $ , are degenerate in finite systems at specific frustration $J 1/ J 2$ . Level crossing extrapolates in the thermodynamic limit to the same critical points as $q_{G}$ . The $S (q)$ peak diverges at $q_{G} = I ¨ $ in the gapless phase with $J 1/ J 2 > 4.148$ and quasi-long-range order (QLRO({ $I ¨ $ })). $S (q)$ diverges at $\pm I ¨ /2$ in the decoupled phase with QLRO({ $I ¨ $ }/2), but is finite in gapped phases with finite range correlations. Numerical results and field theory agree at small $J 2/ J 1$ but disagree for the decoupled phase with weak exchange $J 1$ between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO({ $I ¨ $ }/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

34 pages and 8 figures, To be published in Journal of Physics: Condensed Matter