Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems

Abstract

The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.

References in corpus (12)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Rise and fall of hidden string order of lattice bosons
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Distinct trivial phases protected by a point-group symmetry in quantum spin chains
• Coefficients of bosonized dimer operators in spin-1/2 XXZ chains and their applications
• Geometric phases and the magnetization process in quantum antiferromagnets
• Dimer correlation amplitudes and dimer excitation gap in spin-1/2 XXZ and Heisenberg chains
• Quantitative expression of the spin gap via bosonization for a dimerized spin-1/2 chain
• Symmetry-protected topological order in magnetization plateau states of quantum spin chains
• Polarization amplitude near quantum critical points