Rigorous proof for the non-local correlation functions in the antiferromagnetic seamed transverse Ising ring

Abstract

An unusual correlation function is conjectured by M. Campostrini et al. (Phys. Rev. E 91, 042123 (2015)) for the ground state of a transverse Ising chain with geometrical frustration in one of the translationally invariant cases. Later, we demonstrated the correlation function and showed its non-local nature in the thermodynamic limit based on the rigorous evaluation of a Toeplitz determinant (J. Stat. Mech. 113102 (2016)). In this paper, we prove rigorously that all the states that forming the lowest gapless spectrum (including the ground state) in the kink phase exhibit the same asymptotic correlation function. So, in a point of view of cannonical ensemble, the thermal correlation function is inert to temperature within the energy range of the lowest gapless spectrum.

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References in corpus (6)

• An introduction to integrable techniques for one-dimensional quantum systems
• Quantum transitions driven by one-bond defects in quantum Ising rings
• The A-Cycle Problem for Transverse Ising Ring
• The A-Cycle Problem In XY model with Ring Frustration
• Haldane-like antiferromagnetic spin chain in the large anisotropy limit
• Antiferromagnetic molecular nanomagnets with odd-numbered coupled spins

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• Towards a phase diagram of the topologically frustrated XY chain
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• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• Ring-Frustrated Non-Hermitian $XY$ Model
• Impurity-driven transitions in frustrated quantum Ising ring
• Nonlocal behaviors of spin correlations in the Haldane-Shastry model
• Quantum cluster kink and ring frustration