From Quantum Spin Chains to Chiral Spin Liquids

Abstract

Chiral spin liquids are highly entangled phases of matter in which interacting spins break time reversal and reflection symmetries, but do not develop magnetic order even at zero temperature. The conventional analytical approach to describe quantum spin liquids employs parton representations for the spin operator, but the resulting gauge theories are hard to handle beyond mean-field approximations. In this chapter, we review an alternative approach that starts from the conformal field theory for weakly coupled Heisenberg spin chains. We provide two examples of such coupled-chain constructions. The first one is the Kalmeyer–Laughlin chiral spin liquid, a gapped topological phase that can be obtained by coupling parallel spin chains with three-spin interactions that favor uniform spin chirality. The second example is a gapless chiral spin liquid on a geometry of crossed chains with a staggered chirality pattern. Using a renormalize group analysis, we identify the conditions necessary to stabilize these nontrivial phases and discuss how to calculate their properties explicitly at the low-energy fixed points.