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

Abstract

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 is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 ≈ 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in halffilled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA = NB. The ground state (GS) and spin densities ρr =< S z r > at site r are quite different for junctions with S = 1/2, 1, 3/2 and 2. The GS has finite total spin SG = 2S(S) for even (odd) N and for MG = SG in the SG spin manifold, ρr > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N . S = 1 junctions have four localized Sz = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave (SDW) with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

“…61,62 For accurate calculations we have used the modified DMRG algorithm especially designed for Y junction, which renders the accuracy of these calculations comparable to that for linear 1D chains. 52 To maintain a reliable accuracy in the calculations, eigenvectors corresponding to up to 200 largest eigenvalues are retained in each DMRG sweep. The truncation error of the density matrix eigenvalues is less than 10 −12 .…”

“…18,21,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] The ground state properties of Y junctions have also been explored using density matrix renormalization group (DMRG) techniques. [51][52][53] A study of TDOS using bosonization technique for spinless fermion was reported by Agarwal et al in Ref. [18] and a collection of FPs (stable for g > 1) were identified which showed enhancement of TDOS in the zero energy limit and the effect was attributed to an Andreev-like reflection off the junction.…”

Boundary-induced spin-density waves in linear Heisenberg antiferromagnetic spin chains withS≥1

“…18 Y junctions of N = 3n + 1 spins have three arms of n spins plus a central site for which we recently presented an efficient DMRG algorithm. Fig.…”

“…2 of Ref. 18 shows the growth of the infinite DMRG algorithm. A chain of N = 2n + 1 spins can be viewed as two arms of n spins plus a central site.…”

“…18 In either algorithm, new sites are coupled to the most recently added sites and the superblock Hamiltonian contains only new and once renormalized operators. Table I has representative DMRG results for the ground states of S = 2 and 3/2 chains with N ≥ 100 spins.…”