Theory of competing Chern-Simons orders and emergent phase transitions

Abstract

Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a systematic framework to investigate the competition between emergent phases in frustrated two-dimensional XY quantum magnets. Application of the method to the antiferromagnetic honeycomb spin-1/2 $J_1$-$J_2$ XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid that was proposed earlier in the literature. Namely, the Chern-Simons superconductor describes the planar Néel state, while the Chern-Simons exciton insulator corresponds to the non-uniform chiral spin-liquid. These results are further confirmed by our high-precision tensor network calculation, which provides the first numerical evidence for the transition from Néel order to a non-uniform chiral spin-liquid. We argue that the developed method can be applied to other frustrated quantum magnets of XXZ type and can detect unconventional phase transitions.

15 pages, 8 figures, supplemental material included

References in corpus (16)

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• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
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• Accurate determination of tensor network state of quantum lattice models in two dimensions
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• Algorithms for finite Projected Entangled Pair States
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
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• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Topological spin ordering via Chern-Simons superconductivity
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• Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice

Cited by in corpus (15)

• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation
• Efficient calculation of three-dimensional tensor networks
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Demystifying quantum escapism on the honeycomb lattice
• Quantization and quantum oscillations of the sublattice charge order in Dirac insulators
• Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states
• Correlated phases of moat-band excitons in two dimensions
• Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method