Polarization amplitude near quantum critical points

Abstract

We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the U(1) flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.

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Cited by in corpus (10)

• Scaling and renormalization in the modern theory of polarization: application to disordered systems
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Bosonization with a background $U(1)$ gauge field
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Diagnosing energy gap in quantum spin liquids via polarization amplitude
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems