Projective symmetry group classification of chiral spin liquids

Abstract

We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then introduce a systematic generalization of the approach for symmetric $\mathbb{Z}_2$ quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral $\mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.Comment: 21+7 pages, 9 figs, 9 tabs; published versio

Doping-induced redistribution of magnetic spectral weight in the substituted hexaborides Ce1−xLaxB6 and Nikitin1, Portnichenko2, Dukhnenko3 et al. 2018Phys. Rev. B123160View full textAdd to dashboardCite

“…This is why frustrated magnets usually exhibit complex magnetic phase diagrams in which multiple thermodynamic phases are found in close proximity [99][100][101][102][103]. Our present results indicate that the similarly rich phase diagram of Ce 1−x Nd x B 6 and Ce 1−x La x B 6 , which comprises at least two different multipolar phases and a number of AFM phases, could be the result of a similar competition among different Fermi-surface nesting vectors, where the charge-carrier doping and magnetic-moment concentration play the role of tuning parameters.…”

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

“…In Fig. 1(b), we show the Ansatz of the variational wave function [71]. Since the requirement of t * ij = t ji , we define the orientation of the hoping terms in this way: for the hopping from j to i, t ij (t * ij ) has the direction (opposite direction) along the arrow shown in Fig.…”

Spinon Fermi surface U(1) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO4

“…With the extended Nambu spinor, the spin operator S r and the generator G r for the SU(2) gauge transformation are given by 47,[50][51][52][53] …”