Excited States in Spin Chains from Conformal Blocks

Abstract

We develop a method of constructing excited states in one dimensional spin chains which are derived from the $SU(2{)}_1$ Wess-Zumino-Witten Conformal Field Theory (CFT) using a parent Hamiltonian approach. The resulting systems are equivalent to the Haldane-Shastry model. In our ansatz, correlation functions between primary fields correspond to the ground state of the spin system, whereas excited states are obtained by insertion of descendant fields. Our construction is based on the current algebra of the CFT and emphasizes the close relation between the spectrum of the spin system and the underlying CFT. This general structure might imply that the method could be applied to a wider range of model systems.

15 pages, 4 figures, v2: significantly improved, v3: accepted version

References in corpus (14)

• Mayavi: a package for 3D visualization of scientific data
• Topological Order and Conformal Quantum Critical Points
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• Yangian Symmetry in Conformal Field Theory
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Infinite Matrix Product States for long range SU(N) spin models
• Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
• Integrability and Applications of the Exactly-Solvable Haldane-Shastry One-Dimensional Quantum Spin Chain

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• Disordered Haldane-Shastry model
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