Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain

Abstract

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 $D$. This model presents a critical line separating the gaped Haldane and large-$D$ 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 with the standard scaling holding in the Ising-like transition between the gapless AF-Néel and gaped Haldane phases. Our results are compared with field-theoretic predictions and available high-accuracy data for specific points along the Gaussian line.

9 pages, 14 figures

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Matrix Product State applications for the ALPS project
• Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
• On $c=1$ critical phases in anisotropic spin-1 chains
• Fidelity approach to Gaussian transitions
• Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
• Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid
• Quantum phase transitions in the dimerized extended Bose-Hubbard model
• All spin-1 topological phases in a single spin-2 chain
• Finite Size Scaling of Topological Entanglement Entropy
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases

Cited by in corpus (3)

• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• Exploring quantum phase transitions by the cross derivative of the ground state energy
• Deconfined quantum criticality in a frustrated Haldane chain with single-ion anisotropy