Ground state and low-lying excitations in the Heisenberg XXZ chain of arbitrary spin S

Sogo, Kiyoshi

doi:10.1016/0375-9601(84)90588-7

Cited by 78 publications

(57 citation statements)

References 14 publications

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“…The integrable spin-s generalization of the XXZ spin chain and related R-matrices have been studied by many authors; amongst them [11,12,3,13,14,15,16,17,8] . In particular, the spin-1 Hamiltonian was first constructed in Ref.…”

Section: Spin-s Xxz Quantum Chainsmentioning

confidence: 99%

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

Yung

Batchelor

1995

Nuclear Physics B

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We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on "pair-propagation through a vertex". The Bethe ansatz-type equations obtained reduce, in the case of lattice size N = 1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.Running title: Spin-s XXZ chain with twists

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Section: Spin-s Xxz Quantum Chainsmentioning

confidence: 99%

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

Yung

Batchelor

1995

Nuclear Physics B

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“…We continue to follow [12][13][14][15] and [23][24][25][26][27] by taking the logarithm of (3.4). This introduces integers or half integers [28] as the various branches of ln 1 or ln(−1).…”

Section: B Rules For V Lmentioning

confidence: 99%

“…In section 3 we present the rules which count the states, and in the appendix demonstrate that these rules are complete. These counting rules, indeed, have a very interesting relation to the S = 1 XXZ model [9][10][11][12][13][14][15] with anisotropy parameter γ = π/3 which we discuss in section 4. In section 5 we compute all the low-lying excitations in the massive phase.…”

Section: Introductionmentioning

confidence: 99%

Spectrum and completeness of the three-state superintegrable chiral Potts model

Dasmahapatra¹,

Kedem²,

McCoy³

1993

Nuclear Physics B

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We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitations is compared with the BCS superconductivity spectrum and the counting rules are compared with the closely related S = 1 XXZ spin chain.

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“…where v s = Jπ/2 coincides with the known spin velocity [40] and c(k) is nothing but the central charge of level-k SU(2) WZWN model. This is the desired result from the WZWN description of massless quantum spin chains.…”

Section: Analytic Evaluation Of the Low Temperature Asymptoticsmentioning

confidence: 99%

Spinons in magnetic chains of arbitrary spins at finite temperatures

Suzuki

1999

J. Phys. A: Math. Gen.

213

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The thermodynamics of solvable isotropic chains with arbitrary spins is addressed by the recently developed quantum transfer matrix (QTM) approach. The set of nonlinear equations which exactly characterize the free energy is derived by respecting the physical excitations at T = 0, spinons and RSOS kinks. We argue the implication of the present formulation to spinon character formula of level k = 2S SU(2) WZWN

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Ground state and low-lying excitations in the Heisenberg XXZ chain of arbitrary spin S

Cited by 78 publications

References 14 publications

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

Spectrum and completeness of the three-state superintegrable chiral Potts model

Spinons in magnetic chains of arbitrary spins at finite temperatures

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