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.

arXiv comment8 pages, 0 figures

References in corpus (10)

• Dynamics of quantum phase transition: exact solution in quantum Ising model
• An introduction to integrable techniques for one-dimensional quantum systems
• Quantum transitions driven by one-bond defects in quantum Ising rings
• Quantum Ising chains with boundary fields
• Frustration, Entanglement, and Correlations in Quantum Many Body Systems
• The A-Cycle Problem for Transverse Ising Ring
• Anomalous behavior of the energy gap in the one-dimensional quantum XY model
• 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

Cited by in corpus (13)

• Quantum Phase Transition induced by Topological Frustration
• Effects of defects in the XY chain with frustrated boundary conditions
• Ring frustration and factorizable correlation functions of critical spin rings
• Functional field integral approach to quantum work
• Long-range entanglement and topological excitations
• Topological Frustration can modify the nature of a Quantum Phase Transition
• Towards a phase diagram of the topologically frustrated XY chain
• Asymptotic behavior of Toeplitz determinants with a delta function singularity
• 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