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.

arXiv comment15 pages, 8 figures, supplemental material included

References in corpus (66)

• Anyons in an exactly solved model and beyond
• Area laws for the entanglement entropy - a review
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Generalized Global Symmetries
• Topological orders and Edge excitations in FQH states
• Quantum Orders and Symmetric Spin Liquids
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Corner Transfer Matrix Renormalization Group Method
• Coarse-graining renormalization by higher-order singular value decomposition
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• The Flux-Phase of the Half-Filled Band
• Deconfined quantum critical points: symmetries and dualities
• A symmetry principle for Topological Quantum Order
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Stability and phase coherence of trapped 1D Bose gases
• Hidden order in 1D Bose insulators
• Bose condensation in flat bands
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Rise and fall of hidden string order of lattice bosons
• Algorithms for finite Projected Entangled Pair States
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Symmetry and Topological Order
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Deconfined quantum criticality and Neel order via dimer disorder
• Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices
• Excitonic Phases from Weyl Semi-Metals
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Projective symmetry group classification of chiral spin liquids
• Topological Phase Transitions for Interacting Finite Systems
• Kaleidoscope of exotic quantum phases in a frustrated XY model
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Emmy Noether looks at the deconfined quantum critical point
• Absence of Bose condensation on lattices with moat bands
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 $J_1-J_2$ XY Model on the Honeycomb Lattice
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Chern_simons Theory of the Anisotropic Quantum Heisenberg Antiferromagnet on a Square Lattice
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Fermionization of Bosons in a Flat Band
• Topological spin ordering via Chern-Simons superconductivity
• Nature of the phases in the frustrated XY model on the honeycomb lattice
• Continuous phase transition from Néel state to Z_2 spin liquid state on a square lattice
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• A generalized Lanczos method for systematic optimization of tensor network states
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
• Chern-Simons superconductors and their instabilities
• Antiferromagnetic magnons from fractionalized excitations
• Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory
• Is the composite fermion state of Graphene a doped Chern insulator?
• Emergent Kondo behavior from gauge fluctuations in spin liquids
• Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice

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• 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