Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective

Abstract

Recently, in the Luttinger liquid phase of the one-dimensional generalized antiferromagnetic Kitaev spin-1/2 model, it has been found that the abelian bosonization formulas of the local spin operators only respect the exact discrete nonsymmorphic symmetry group of the model, not the emergent U(1) symmetry. In this work, we perform a renormalization group (RG) study to provide explanations for the origin of the U(1) breaking terms in the bosonization formulas. We find that the lack of U(1) symmetry originates from the wavefunction renormalization effects in the spin operators along the RG flow induced by the U(1) breaking interactions in the microscopic Hamiltonian. In addition, the RG analysis can give predictions to the signs and order of magnitudes of the coefficients in the bosonization formulas. Our work is helpful to understand the rich nonsymmorphic physics in one-dimensional Kitaev spin models.

arXiv comment21 pages, 8 figures

References in corpus (44)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Correlated quantum phenomena in the strong spin-orbit regime
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Phase Diagram of $\alpha$-RuCl${}_3$ in an in-plane Magnetic Field
• Gapless Spin Excitations in the Field-Induced Quantum Spin Liquid Phase of alpha-RuCl3
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet $\alpha$-RuCl${}_3$
• Field-induced quantum criticality in the Kitaev system $\alpha$-RuCl${}_3$
• Theoretical investigation of the magnetic dynamics in $\alpha$-RuCl${}_3$
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Critical properties of the Kitaev-Heisenberg model
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Classical spin liquid instability driven by off-diagonal exchange in strong spin-orbit magnets
• Path to stable quantum spin liquids in spin-orbit coupled correlated materials
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• The Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
• Non-local String Order Parameter in the $S=1/2$ Kitaev-Heisenberg Ladder
• Phase diagram of the spin-1/2 Kitaev-Gamma chain and emergent SU(2) symmetry
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Unveiling the phase diagram of a bond-alternating spin-$\frac{1}{2}$ $K$-$\Gamma$ chain
• Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb
• Comprehensive study of the phase diagram of the spin-1/2 Kitaev-Heisenberg-Gamma chain
• Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain
• Lifshitz phase transitions in one-dimensional Gamma model
• Classical spin order near antiferromagnetic Kitaev point in the spin-1/2 Kitaev-Gamma chain
• Spin wave theory of one-dimensional generalized Kitaev model
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders

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• Spin dynamics of the generalized quantum spin compass chain
• Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain
• Emergent SU(2)${}_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models