Spin Chain Network Construction of Chiral Spin Liquids

Abstract

We show that a honeycomb lattice of Heisenberg spin-1/2 chains with three-spin junction interactions allows for controlled analytical studies of chiral spin liquids (CSLs). Tuning these interactions to a chiral fixed point, we find a Kalmeyer-Laughlin CSL phase which here is connected to the critical point of a boundary conformal field theory. Our construction directly yields a quantized spin Hall conductance and localized spinons with semionic statistics as elementary excitations. We also outline the phase diagram away from the chiral point where spinons may condense. Generalizations of our approach can provide microscopic realizations for many other CSLs. Introduction.-Chiral spin liquids occupy a prominent position among the most exotic quantum phases of matter [1]. As examples of quantum spin liquids [2, 3], they occur in magnetic insulators with long-rangeentangled ground states that break time-reversal and reflection symmetries. The historically first proposal is the Kalmeyer-Laughlin CSL [4, 5], a topological phase of interacting spins equivalent to a bosonic fractional quantum Hall state. The non-Abelian phase of Kitaev's honeycomb model in a magnetic field provides another CSL example, with Ising anyons as elementary excitations [6]. Recent experiments have reported a quantized thermal Hall conductance for the Kitaev material α-RuCl 3 [7], compatible with the chiral Majorana edge mode expected for this CSL phase. Various other CSL phases have been theoretically investigated [8-22] and are actively searched for in experiments, including gapless CSLs with spinon Fermi surfaces [23-26].A major obstacle to the theory of CSLs comes from the shortage of analytical methods able to predict their occurrence and their physical properties in microscopic models. Apart from exactly solvable models [6,9,10], standard approaches employ parton mean-field theories that fractionalize the spin operator into fermionic or bosonic quasiparticles [5,27], or use variational wave functions obtained by a Gutzwiller projection scheme [2]. Such approaches are often able to capture the basic phenomenology when the CSL phase is indeed realized. However, since they rely on uncontrolled approximations, their predictions are often questionable, e.g., due to the neglect of interactions mediated by emergent gauge fields. In this Letter we establish a connection between chiral fixed points of boundary conformal field theory (BCFT) [28,29] and CSL phases, and use it to formulate a controlled analytical construction scheme for CSLs where chiral junctions of multiple spin chains serve as the elementary building blocks in two-dimensional (2D) networks of spin chains. Our approach markedly differs from standard coupled-wire constructions [13][14][15][16][30][31][32], where spin liquid phases emerge in models of coupled parallel chains. Our network construction instead uses

Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality

“…Chiral spin liquids (CSLs) [11][12][13] have been extensively studied since Kalmeyer and Laughlin proposed a spin wave function analogous to fractional quantum Hall states [14,15]. The Kalmeyer-Laughlin CSL can be stabilized as the ground state of spin-1/2 models containing chiral three-spin interactions that drive a uniform scalar spin chirality [16][17][18][19][20][21]. In spin-1 models, the same interactions give rise to a non-Abelian CSL analogous to the Moore-Read state [22][23][24].…”

Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model

“…from which we conclude that lim λ→0 κ 3 (λ) = 0 (18) implying that the vector-spin-chirality long range order is excluded.…”

“…Very recently, studying the so-called Y junctions made of spin-1/2 Heisenberg chains, it has been shown that a network of these junctions, with uniform coupling constants, may realize chiral spin liquid phases [16,17]. Remarkably, a controlled analytical investigation of these chiral spin liquid states may be realized by means of a honeycomb lattice of Heisenberg spin-1/2 chains, with three-spin Y junction interactions [18]. Finally, by means a non-abelian symmetry realization of the DM RG technique the behaviour of some chiral correlation functions in isotropic frustrated spin chains with s = 1 and s = 1/2 in an external magnetic field has been studied; it is found that the order does exist in the high field condition, both for s = 1 and s = 1/2 [19].…”

Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

“…Previous suggestions for realizations of spin liquid phases include interaction of three nearest-neighbour spins that breaks time reversal symmetry in the form of a mixed product of three spins (see Refs. [56][57][58][59] and references therein). Instead of having such interactions, our model contains more attainable current-current interactions, and breaks time reversal symmetry by the use of IQH islands.…”