Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

摘要: An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of $n$ sites that meet at a central site. The accuracy comparable DMRG chains. As in chains, new are always bonded the most recently added superblock Hamiltonian contains only or once renormalized operators. Junctions up $N=3n+1\ensuremath{\approx}500$ studied antiferromagnetic (AF) Heisenberg exchange $J$ between nearest-neighbor spins $S$ electron transfer $t$ nearest neighbors half-filled Hubbard models. Exchange exclusively two sublattices ${N}_{A}\ensuremath{\ne}{N}_{B}$. ground state (GS) spin densities ${\ensuremath{\rho}}_{r}=\ensuremath{\langle}{S}_{r}^{z}\ensuremath{\rangle}$ site $r$ quite different for junctions $S=1/2$, 1, 3/2, 2. GS has finite total ${S}_{G}=2S(S)$ even (odd) $N$ ${M}_{G}={S}_{G}$ ${S}_{G}$ manifold, ${\ensuremath{\rho}}_{r}g0(l0)$ larger (smaller) sublattice. $S=1/2$ have delocalized states decreasing increasing $N$. $S=1$ four localized ${S}_{z}=1/2$ end each arm centered on junction, consistent chains Haldane gap. $S=3/2$ 2 500 wave increased amplitude ends near junction. Quantum fluctuations completely suppress AF order 1 as well but reduce rather than junctions.