Spin-1/2 string correlations and singlet-triplet gaps of frustrated ladders with ferromagnetic (F) legs and alternate F and AF rungs

Monalisa Chatterjee; Manoranjan Kumar; ZoltÃ¡n G. Soos

paper

Spin-1/2 string correlations and singlet-triplet gaps of frustrated ladders with ferromagnetic (F) legs and alternate F and AF rungs

arXiv:2403.05238

Abstract

The frustrated ladder with alternate ferromagnetic(F) exchange $- J_{F}$ and AF exchange $J_{A}$ to first neighbors and F exchange $- J_{L}$ to second neighbors is studied by exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations in systems of $2 N$ spins-1/2 with periodic boundary conditions. The ground state is a singlet $(S = 0)$ and the singlet-triplet gap $ε_{T}$ is finite for the exchanges considered. Spin-1/2 string correlation functions $g_{1} (N)$ and $g_{2} (N)$ are defined for an even number $N$ of consecutive spins in systems with two spins per unit cell; the ladder has string order $g_{2} (\infty) > 0$ and $g_{1} (\infty) = 0$ . The minimum $N^{*}$ of $g_{2} (N)$ is related to the range of ground-state spin correlations. Convergence to $g_{2} (\infty)$ is from below, and $g_{1} (N)$ decreases exponentially for $N \geq N^{*}$ . Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of $J_{F}$ , $J_{L}$ and $J_{A}$ reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the $J_{1} - J_{2}$ model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-1/2 systems. The nondegenerate singlet ground state of ladder is a bond-order wave, a KekulÃ© VB diagrams at $J_{L} = J_{F} /2 \leq J_{A}$ , that is reversed on interchanging $- J_{F}$ and $J_{A}$ . Inversion symmetry is spontaneously broken in the dimer phase of the $J_{1} - J_{2}$ model where the KekulÃ© diagrams are the doubly degenerate ground states at $J_{2} / J_{1} = 1/2$ .

12 pages, 11 figures