Ring frustration and factorizable correlation functions of critical spin rings

Abstract

Basing on the exactly solvable prototypical model, the critical transverse Ising ring with or without ring frustration, we establish the concept of nonlocality in a many-body system in the thermodynamic limit by defining the nonlocal factors embedded in its factorizable correlation functions. In the context of nonlocality, the valuable traditional finite-size scaling analysis is reappraised. The factorizable correlation functions of the isotropic $XY$ and the spin-1/2 Heisenberg models are also demonstrated with the emphasis on the effect of ring frustration.

15 pages, 4 figures

References in corpus (17)

• An introduction to integrable techniques for one-dimensional quantum systems
• The Importance of being Odd
• Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain
• Quantum transitions driven by one-bond defects in quantum Ising rings
• Characterizing and Quantifying Frustration in Quantum Many-Body Systems
• Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings
• Quantum Ising chains with boundary fields
• Local and nonlocal order parameters in the Kitaev chain
• Probing Quantum Frustrated Systems via Factorization of the Ground State
• Frustration, Entanglement, and Correlations in Quantum Many Body Systems
• The A-Cycle Problem for Transverse Ising Ring
• Frustration, interaction strength and ground-state entanglement in complex quantum systems
• The boundary effects of transverse field Ising model
• Monogamy and ground-state entanglement in highly connected systems
• The A-Cycle Problem In XY model with Ring Frustration
• Rigorous proof for the non-local correlation functions in the antiferromagnetic seamed transverse Ising ring
• Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions

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• Effects of defects in the XY chain with frustrated boundary conditions
• Lower Bounding Ground-State Energies of Local Hamiltonians Through the Renormalization Group
• Topological Frustration can modify the nature of a Quantum Phase Transition
• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• Impurity-driven transitions in frustrated quantum Ising ring
• Ring-Frustrated Non-Hermitian $XY$ Model
• Quantum Coherence of Topologically Frustrated Spin Chains
• Nonlocal behaviors of spin correlations in the Haldane-Shastry model
• Quantum cluster kink and ring frustration