Exact physical quantities of a competing spin chain in the thermodynamic limit

We study the exact physical quantities of a competing spin chain which contains many interesting and meaningful couplings including nearest neighbor, next chiral three spins, Dzyloshinsky-Moriya interactions unparallel boundary magnetic fields in thermodynamic limit. obtain density zero roots, surface energies elementary excitations different regimes model parameters. Due to competition various interactions, energy excited spectrum show pictures from those Heisenberg chain.