Physical Review Letters

Low-Lying Eigenstates of the One-Dimensional Heisenberg Ferromagnet for any Magnetization and Momentum

Bill Sutherland

Published Jan 30, 1995• 80 citations

Abstract

I present the exact dispersion relations for certain low-lying states of the one-dimensional Heisenberg ferromagnet. These states are bound complexes of $M$ overturned spins, and in fact are the states with the lowest energy for given values of the total spin, $z$ component of spin and momentum.

DOI: 10.1103/physrevlett.74.816

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Physical Review Letters

Low-Lying Eigenstates of the One-Dimensional Heisenberg Ferromagnet for any Magnetization and Momentum

Bill Sutherland

Published Jan 30, 1995• 80 citations

Publisher

Abstract

I present the exact dispersion relations for certain low-lying states of the one-dimensional Heisenberg ferromagnet. These states are bound complexes of

M

overturned spins, and in fact are the states with the lowest energy for given values of the total spin,

z

component of spin and momentum.

DOI: 10.1103/physrevlett.74.816

Related papers

One-Dimensional Heisenberg Model. I: Exact Spin Eigenstates

T. Kebukawa

Progress of Theoretical PhysicsJul 1, 19851 citation

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

Lars Kecke, Tsutomu Momoi, Akira Furusaki

We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions in a magnetic field. Starting from the fully polarized high-field state, we calculate the dispersions of the lowest-lying $n$ -magnon excitations and the saturation field $(n=2,3,4)$ . We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of $\ensuremath{\pi}$ except for a small parameter range. We argue that Bose condensation of the bound $n$ magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to $n=2$ and $n=3$ .We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions in a magnetic field. Starting from the fully polarized high-field state, we calculate the dispersions of the lowest-lying $n$-magnon excitations and the saturation field $(n=2,3,4)$. We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of $\ensuremath{\pi}$ except for a small parameter range. We argue that Bose condensation of the bound $n$ magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to $n=2$ and $n=3$.

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Physical Review BNov 11, 20047 citations

I present the exact dispersion relations for certain low-lying states of the one-dimensional Heisenberg ferromagnet. These states are bound complexes of

M

overturned spins, and in fact are the states with the lowest energy for given values of the total spin,

z

component of spin and momentum.

n

-magnon excitations and the saturation field

(n=2,3,4)

. We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of $\ensuremath{\pi}$ except for a small parameter range. We argue that Bose condensation of the bound

n

magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to

n=2

and

n=3

V

in a similar manner to those of the ferromagnetic model, i.e., $\ensuremath{\Delta}E\ensuremath{\propto}J{L}^{{\ensuremath{\theta}}_{L}}{V}^{{\ensuremath{\theta}}_{v}}$ with ${\ensuremath{\theta}}_{L}\ensuremath{\sim}\ensuremath{-}4.7$ and ${\ensuremath{\theta}}_{v}\ensuremath{\sim}2.0$. This fact suggests that similarity exists in the ground state structure between the $\ifmmode\pm\else\textpm\fi{}J$ and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.