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arXiv:2512.14075 · Physical review. B./Physical review. B

Correlation functions at the topological quantum phase transition in the S = 1 XXZ chain with single-ion anisotropy

Toshiya Hikihara, Akira Furusaki

Published Feb 27, 2026• 0 citations
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Abstract

We study the one-dimensional S=1 XXZ spin model with single-ion anisotropy. It is known that at the transition points between the Haldane and large-D phases, the model exhibits a quantum criticality described by the Gaussian theory, i.e., a conformal field theory with the central charge c=1. Using the bosonization approach, we investigate various correlation functions at the phase transition and derive their asymptotic forms. This allows us to clarify their peculiar behavior: the longitudinal (transverse) two-point spin correlation function has components that decay algebraically only in the uniform (staggered) sector. These theoretical predictions are verified by the numerical calculations using the density-matrix renormalization group method. The effect of weak bond alternation on the critical ground state at the phase transition is also discussed. It is shown that the bond alternation induces the missing power-law components in the correlation functions.

DOI
10.1103/spgd-r3ht

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Scaling aspects of Gaussian topological phase transitions in quantum spin chains are investigated using the prototypical one-dimensional spin-1 XXZ Heisenberg model with uniaxial single-ion anisotropy DDD. This model presents a critical line separating the gapped Haldane and large-DDD phases, with the relevant energy gap closing at the transition point. We show that a proper tangential finite-size scaling analysis is able to accurately locate the Gaussian critical line and to probe the continuously varying set of correlation length critical exponents. The specific features of the tangential scaling are highlighted, in contrast to the standard scaling holding in the Ising-like transition between the gapless antiferromagnetic N\'eel and gapped Haldane phases. Our results are compared with field-theoretic predictions and available high-accuracy data for specific points along the Gaussian line.
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