Infinite Matrix Product States for long range SU(N) spin models

Abstract

We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models.

37 pages, 6 figures

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Cited by in corpus (5)

• Full counting statistics in the Haldane-Shastry chain
• Excited States in Spin Chains from Conformal Blocks
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Entanglement properties of the two-dimensional SU(3) AKLT state
• The BCS wave function, matrix product states, and the Ising conformal field theory