Two-magnon states of the alternating ferromagnetic Heisenberg chain

Bell, S C; Loly, P. D.; Southern, B. W.

doi:10.1088/0953-8984/1/49/010

Cited by 14 publications

(37 citation statements)

References 11 publications

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“…Bell et al 20 studied the two-magnon spectrum of the alternating bond Sϭ 1 2 Heisenberg chain and found a total of four two-magnon bound state branches compared to the uniform chain which only has one branch. Medved et al 6 studied higher spin models and found that an additional bound state branch appears when the spin magnitude is increased to Sϭ1.…”

Section: Resultsmentioning

confidence: 99%

“…Comparison of our results to the known analytical results of Bethe 9,10 for the SϭSЈϭ1/2 chain with homoge-neous bonds indicate complete agreement. We extended the study of Bell et al 20 of the alternating bond Sϭ1/2 twomagnon spectrum to the three-magnon problem. When a bond alternation is introduced, gaps immediately appear and additional bound states are found.…”

Section: Discussionmentioning

confidence: 98%

“…The other set will be called the ''interacting equations'' and will involve amplitudes with spin deviations on the same or neighboring sites. It can easily be shown 6,19,20 that the energy eigenvalues are simply the sum of the energy of two noninteracting magnons…”

Section: B Two-magnon Excitationsmentioning

confidence: 99%

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Multimagnon excitations in alternating spin/bond chains

1998

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The nature of multimagnon excitations in alternating spin/bond ferromagnetic chains are studied using a combination of scaling methods and the recursion method. Two-magnon excitations for a Heisenberg chain with either alternating spin magnitudes, S and SЈ, or alternating nearest-neighbor couplings, J 1 and J 2 can be studied using real-space rescaling techniques. These results are then used to investigate three-magnon excitations using the recursion method. ͓S0163-1829͑98͒02038-6͔

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 98%

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Multimagnon excitations in alternating spin/bond chains

1998

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“…the corresponding one-and two-magnon states may be obtained by standard analysis [9,10,11,12]. The Q-magnon states with Q > 2 are known only for a rare class of integrable models [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…That is why the expansion (6), (7) is a low-temperature expansion, while the expansion (11), (12) due to the well known theorem [19] lim…”

Section: Introductionmentioning

confidence: 99%

Second cluster integral from the spectrum of an infinite XXZ spin chain

Bibikov

2015

Annals of Physics

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First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized XXZ spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one-and two-magnon infinite-chain spectrums. In the XXXpoint the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.

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Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

Pomoni¹,

Rabe

Zoubos

2021

J. High Energ. Phys.

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This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $$ \mathcal{N} $$ N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the $$ \mathcal{N} $$ N = 4 symmetry algebra down to the $$ \mathcal{N} $$ N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the ℤ2 quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.

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Two-magnon states of the alternating ferromagnetic Heisenberg chain

Cited by 14 publications

References 11 publications

Multimagnon excitations in alternating spin/bond chains

Multimagnon excitations in alternating spin/bond chains

Second cluster integral from the spectrum of an infinite XXZ spin chain

Dynamical spin chains in 4D $$ \mathcal{N} $$ = 2 SCFTs

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