XXX Heisenberg s1{2 model has been examined in detail during last decades, however, recently one may find some new insights into that issue.Among several approaches describing the eigenproblem for the finite case, a close look into the structure of Bethe equations (BE) for the two-magnon sector case seems to be particularly interesting.BE enable us to evaluate parameters labeling eigenstates of a magnet, however to find appropriate sets of winding numbers, which parametrize BE, one has to apply the Inverse Bethe Ansatz method.On the other hand, one may choose a different -combinatoric approach -which also parametrizes Bethe eigenstates, with the use of rigging numbers describing string configurations.We present an idea of comparison of the concepts mentioned above for the particular case of two-spin deviations sector.XXX Heisenberg s1{2 model has been examined in detail during last decades, however, recently one may find some new insights into that issue.Among several approaches describing the eigenproblem for the finite case, a close look into the structure of Bethe equations (BE) for the two-magnon sector case seems to be particularly interesting.BE enable us to evaluate parameters labeling eigenstates of a magnet, however to find appropriate sets of winding numbers, which parametrize BE, one has to apply the Inverse Bethe Ansatz method.On the other hand, one may choose a different -combinatoric approach -which also parametrizes Bethe eigenstates, with the use of rigging numbers describing string configurations.We present an idea of comparison of the concepts mentioned above for the particular case of two-spin deviations sector.

Acta Physica Polonica AMar 1, 20184 citations

Three magnon bound states

Chanchal K. Majumdar, Goutam Mukhopadhyay

Physics Letters AMar 1, 19707 citations

Eigenstates, Eigenvalues

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert

Compendium of Quantum PhysicsJan 1, 20090 citations

Stationary and dynamical aspects of two-magnon states in disordered ferromagnetic chains

Elton Malta Nascimento, F. A. B. F. de Moura, M. L. Lyra

We study the nature of collective two-spin excitations in disordered $S=1∕2$ ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.We study the nature of collective two-spin excitations in disordered $S=1∕2$ ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.

Physical Review BDec 14, 20053 citations

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

Steven R. White, David A. Huse

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 ${\mathit{e}}_{0}$ \ensuremath{\simeq}-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 \ensuremath{\xi}\ensuremath{\simeq}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(\ensuremath{\infty})\ensuremath{\simeq}-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=\ensuremath{\pi}, is the Haldane gap, which we find to be \ensuremath{\Delta}\ensuremath{\simeq}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 \ensuremath{\pi}, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.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 ${\mathit{e}}_{0}$\ensuremath{\simeq}-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 \ensuremath{\xi}\ensuremath{\simeq}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(\ensuremath{\infty})\ensuremath{\simeq}-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=\ensuremath{\pi}, is the Haldane gap, which we find to be \ensuremath{\Delta}\ensuremath{\simeq}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 \ensuremath{\pi}, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.

Physical review. B, Condensed matterAug 1, 1993605 citations

We study the nature of collective two-spin excitations in disordered

S=1∕2

ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.

{\mathit{e}}_{0}

\ensuremath{\simeq}-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 \ensuremath{\xi}\ensuremath{\simeq}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(\ensuremath{\infty})\ensuremath{\simeq}-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=\ensuremath{\pi}, is the Haldane gap, which we find to be \ensuremath{\Delta}\ensuremath{\simeq}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 \ensuremath{\pi}, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.