TY - JOUR

T1 - Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain

AU - White, Steven R.

AU - Huse, David A.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1993

Y1 - 1993

N2 - We present results of a numerical renormalization-group study of the isotropic S=1 Heisenberg chain. The density-matrix renormalization-group techniques used allow us to calculate a variety of properties of the chain with unprecedented accuracy. The ground-state energy per site of the infinite chain is found to be e0-1.401 484 038 971(4). Open-ended S=1 chains have effective S=1/2 spins on each end, with exponential decay of the local spin moment away from the ends, with decay length 6.03(1). The spin-spin correlation function also decays exponentially, and although the correlation length cannot be measured as accurately as the open-end decay length, it appears that the two lengths are identical. The string correlation function shows long-range order, with g()-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=, is the Haldane gap, which we find to be 0.410 50(2). We find many low-lying excited states, including one- and two-magnon states, for several different chain lengths. The magnons have spin S=1, so the two-magnon states are singlets (S=0), triplets (S=1), and quintuplets (S=2). For magnons with momenta near, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.

AB - We present results of a numerical renormalization-group study of the isotropic S=1 Heisenberg chain. The density-matrix renormalization-group techniques used allow us to calculate a variety of properties of the chain with unprecedented accuracy. The ground-state energy per site of the infinite chain is found to be e0-1.401 484 038 971(4). Open-ended S=1 chains have effective S=1/2 spins on each end, with exponential decay of the local spin moment away from the ends, with decay length 6.03(1). The spin-spin correlation function also decays exponentially, and although the correlation length cannot be measured as accurately as the open-end decay length, it appears that the two lengths are identical. The string correlation function shows long-range order, with g()-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=, is the Haldane gap, which we find to be 0.410 50(2). We find many low-lying excited states, including one- and two-magnon states, for several different chain lengths. The magnons have spin S=1, so the two-magnon states are singlets (S=0), triplets (S=1), and quintuplets (S=2). For magnons with momenta near, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.

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U2 - 10.1103/PhysRevB.48.3844

DO - 10.1103/PhysRevB.48.3844

M3 - Article

AN - SCOPUS:33751276962

VL - 48

SP - 3844

EP - 3852

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 6

ER -