Local parent Hamiltonian for the chiral spin liquid

• Applicant: Privatdozent Dr. Martin Greiter
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 435192211

The chiral spin liquid (CSL), originally proposed by V. Kalmeyer andR.B. Laughlin in 1987 as a possible description of itinerantantiferromagnets (AFs) in the context of CuO superconductivity,remains one of the analytically most accessible spin liquid states andcontinues to draw a significant amount of interest in the condensedmatter community. Spin liquids possess strong, localantiferromagnetic correlations, but no long range order. They supportfractionally quantized excitations, and are usually topologicallyordered. They occur in antiferromagnetic systems in situations wherequantum fluctuations destroy the long range order. This is wellunderstood in models of quantum spin chains, but can also occur intwo-dimensional lattice models, either due to geometric frustration,or due to the enhanced mobility of itinerant charge carriers in spinliquid states. The chiral spin liquid states are given by bosonic,fractionally quantized Hall wave functions for spin flip operators,supplemented by gauge factors. A long standing problem in the fieldis the identification of a local parent Hamiltonian which singles outthe Abelian CSL states for spin 1/2 and the non-Abelian CSL states forhigher spins as exact and (modulo the topological degeneracies onhigher genus surfaces like the torus) non-degenerate ground states.In this project, we wish to derive a family of parent Hamiltonians forthe CSLs from local operators, which annihilate the CSL ground statesbut are neither Hermitian nor invariant under lattice translations orSU(2) spin rotations. The Hamiltonians we seek to derive, bycontrast, have to be Hermitian and should possess the symmetries ofthe ground state. If successful, this work will elevate the CSLs fromuniversality classes specified by trial wave functions to exactlysolvable, local models of two-dimensional quantum AFs, which mighteven be integrable. The models we hope to obtain will enable us andother groups to study the properties of fractional excitations intwo-dimensional AFs on a previously unattained level of rigor.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Ronny Thomale