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arXiv:1906.00807 · Physical Review Letters

Spin Chain Network Construction of Chiral Spin Liquids

Gabriel Ferraz, Flávia B. Ramos, Reinhold Egger, Rodrigo G. Pereira

Published Sep 25, 2019• 18 citations
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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.

DOI
10.1103/physrevlett.123.137202

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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.
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We use junctions of critical spin-1 chains as the basic elements to construct a honeycomb network that harbors a gapless chiral spin liquid phase. The low-energy modes are described by spin-1 Majorana fermions that form a two-dimensional Fermi surface when the interactions at the junctions are tuned to the vicinity of chiral fixed points with staggered chirality. We discuss the physical properties and the stability of this chiral spin liquid phase against perturbations from the point of view of the effective field theory for the network. We find clear connections with the excitation spectrum obtained in parton constructions on the kagome lattice.
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We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin-1/21/21/2 Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin-liquid phases.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.