Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration.
basic_science · Level V
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- Also identified by DOI 10.1103/PhysRevE.97.012133.
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Abstract
An unusual correlation function was conjectured by Campostrini et al. [Phys. Rev. E 91, 042123 (2015)PLEEE81539-375510.1103/PhysRevE.91.042123] for the ground state of a transverse Ising chain with geometrical frustration. Later, we provided a rigorous proof for it and demonstrated its nonlocal nature based on an evaluation of a Toeplitz determinant in the thermodynamic limit [J. Stat. Mech. (2016) 11310210.1088/1742-5468/2016/11/113102]. In this paper, we further prove that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state. As a consequence, the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.