Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models

Abstract

In this work, we perform a detailed study on the consequences of nonsymmorphic symmetries in the Luttinger phase of the one-dimensional spin-1/2 Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Nonsymmorphic bosonization formulas for the spin operators are proposed, containing ten non-universal coefficients which are determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, different Fourier components and decay powers in the correlation functions are disentangled, the response to weak magnetic fields is analyzed, and the zigzag magnetic order in two dimensions is recovered from a system of weakly coupled chains. We also find a line of critical points with an emergent SU(2)${}_1$ conformal symmetry located on the boundary of the Luttinger liquid phase, where a nonabelian version of nonsymmorphic bosonization should be applied.

22 pages, 7 figures

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Lifshitz phase transitions in one-dimensional Gamma model
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders

Cited by in corpus (2)

• 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