2011
DOI: 10.1088/1742-5468/2011/11/p11014
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Quantum spin Hamiltonians for theSU(2)kWZW model

Abstract: Abstract. We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and corresponding ground state wave function(s). The approach is quite general, and we illustrate it by constructing a family of Hamiltonians whose ground states are the chiral correlators of the SU (2) k WZW model for integer values of the level k. The simplest example corresponds to k = 1 and is essentially a nonuniform generalization of the Haldane-Shastry model with long-range exchange c… Show more

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Cited by 84 publications
(162 citation statements)
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“…[8,[22][23][24]), where ρ L is the reduced density matrix of the state in a subsystem of length L. For the SO(n) 1 WZW model with c = n/2 we expect S The origin of the small deviations of the numerical results and the SO(n) 1 predictions may be due to the presence of marginally irrelevant terms in the SO(n) 1 WZW model for (1) and its parent Hamiltonian (5), unlike the SU(n) Haldane-Shastry models [25,26] (including the spin-1/2 Haldane-Shastry model for n = 2) being the fixed points of the SU(n) 1 WZW model. For n = 3, the presence of marginal term in the spin-1 Haldane-Shastry model has been confirmed numerically [9,10]. If this is also the case for n ≥ 5, an interesting open question is whether there exist a modified version of (1) and its parent Hamiltonian that represent the fixed point of the SO(n) 1 WZW model.…”
Section: Fig 1: (Color Online)mentioning
confidence: 90%
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“…[8,[22][23][24]), where ρ L is the reduced density matrix of the state in a subsystem of length L. For the SO(n) 1 WZW model with c = n/2 we expect S The origin of the small deviations of the numerical results and the SO(n) 1 predictions may be due to the presence of marginally irrelevant terms in the SO(n) 1 WZW model for (1) and its parent Hamiltonian (5), unlike the SU(n) Haldane-Shastry models [25,26] (including the spin-1/2 Haldane-Shastry model for n = 2) being the fixed points of the SU(n) 1 WZW model. For n = 3, the presence of marginal term in the spin-1 Haldane-Shastry model has been confirmed numerically [9,10]. If this is also the case for n ≥ 5, an interesting open question is whether there exist a modified version of (1) and its parent Hamiltonian that represent the fixed point of the SO(n) 1 WZW model.…”
Section: Fig 1: (Color Online)mentioning
confidence: 90%
“…[9][10][11]. It was shown [9,10] that this state is critical and its low-energy effective theory is an SU(2) 2 (or equivalently SO(3) 1 ) WZW model.…”
Section: Fig 1: (Color Online)mentioning
confidence: 99%
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