Exact solution of a cluster model with next-nearest-neighbor interaction

Abstract

A one-dimensional cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan-Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.

21 pages, 2 figures, the final version to appear in PTEP

References in corpus (7)

• Identifying phases of quantum many-body systems that are universal for quantum computation
• Criticality in correlated quantum matter
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• MERA for Spin Chains with Continuously Varying Criticality
• Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations
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Cited by in corpus (11)

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• Onsager algebra and algebraic generalization of Jordan-Wigner transformation
• Integrable spin chains and the Clifford group
• Exact real time dynamics with free fermions in disguise
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
• The Hilbert-space structure of free fermions in disguise
• The exact susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
• Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain