Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

Abstract

We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number $C=2$ on square, triangular and kagome lattices. The three CDW order parameters form a manifold of $S^2$ or $S^1$ depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge $2e$ and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a $U(1)$ theory with two bosons, a $U(1)$ theory with two Dirac fermions, and an $SU(2)$ theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The $SU(2)$ theory offers a unified framework for a series of fixed points with explicit $SO(5),O(4)$ or $SO(3)\times O(2)$ symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged $SO(5)$ or $O(4)$ symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase.

arXiv comment30+7 pages, 9 figures, 11 tables

References in corpus (60)

• Quantum Spin Liquids
• Quantum Spin Liquid States
• "Deconfined" quantum critical points
• Quantum Spin Liquids
• Quantum Orders and Symmetric Spin Liquids
• Lieb-Schultz-Mattis in Higher Dimensions
• The Hubbard Model
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Nearly Flat Chern Bands in Moiré Superlattices
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Deconfined quantum critical points: symmetries and dualities
• Continuous Mott transition in semiconductor moiré superlattices
• Level/rank Duality and Chern-Simons-Matter Theories
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Particle-Vortex Duality from 3d Bosonization
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Intrinsic and emergent anomalies at deconfined critical points
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Nature of chiral spin liquids on the kagome lattice
• A Quantum Dipolar Spin Liquid
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• A continuous transition between fractional quantum Hall and superfluid states
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Parent Hamiltonian for the Chiral Spin Liquid
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• Topological superconductivity in the doped chiral spin liquid on the triangular lattice
• Enhanced thermal Hall effect in the square-lattice Néel state
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Continuous Preparation of a Fractional Chern Insulator
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Fractionalized conductivity and emergent self-duality near topological phase transitions
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
• Symmetry fractionalization of visons in ${\mathbb{Z}}_2$ spin liquids
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Deconfined criticality and bosonization duality in easy-plane Chern-Simons two-dimensional antiferromagnets
• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice

Cited by in corpus (8)

• Phase transitions out of quantum Hall states in moiré materials
• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Intertwined fractional quantum anomalous Hall states and charge density waves
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• Chiral spin liquid phase in an optical lattice at mean-field level
• Pathways from a chiral superconductor to a composite Fermi liquid