Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories

Hackenbroich, Anna and Tu, Hong-Hao (2017): Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories. In: Nuclear Physics B, Vol. 916: pp. 1-27

Abstract

We introduce a family of many-body quantum states that describe interacting spin one-half hard-core particles with bosonic or fermionic statistics on arbitrary one- and two-dimensional lattices. The wave functions at lattice filling fraction v = 2/(2m + 1) are derived from deformations of the Wess-Zumino-Witten model su(3)(1) and are related to the (m + 1, m + 1, in) Halperin fractional quantum Hall states. We derive long-range SU(2) invariant parent Hamiltonians for these states which in two dimensions are chiral t-J-V models with additional three-body interaction terms. In one dimension we obtain a generalisation to open chains of a periodic inverse-square t-J-V model proposed in [25]. We observe that the gapless low-energy spectrum of this model and its open-boundary generalisation can be described by rapidity sets with the same generalised Pauli exclusion principle. A two-component compactified free boson conformal field theory is identified as the low-energy effective theory for the periodic inverse-square t-J-V model. (C) 2017 Published by Elsevier B.V.

• Item Type: Journal article
• Faculties: Physics
• Subjects: 500 Science > 530 Physics
• ISSN: 0550-3213
• Language: English