Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition

Abstract

We uncover new topology-related features of the $\pi$-flux saddle-point solution of the $D$=2+1 Heisenberg antiferromagnet. We note that symmetries of the spinons sustain a built-in competition between antiferromagnetic (AF) and valence-bond-solid (VBS) orders, the two tendencies central to recent developments on quantum criticality. An effective theory containing an analogue of the Wess-Zumino-Witten term is derived, which generates quantum phases related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry phases. The theory readily generalizes to $\pi$-flux states for all $D$.

4 pages, revised

References in corpus (2)

• "Deconfined" quantum critical points
• On the stability of U(1) spin liquids in two dimensions

Cited by in corpus (60)

• Generalized Symmetries in Condensed Matter
• Algebraic spin liquid as the mother of many competing orders
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• SU(N) quantum spin models: A variational wavefunction study
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Geometric phases and competing orders in two dimensions
• A square lattice algebraic spin liquid with SO(5) symmetry
• Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Fixed point annihilation for a spin in a fluctuating field
• Effective field theory with a $\theta$-vacua structure for 2d spin systems
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model
• Kondo physics in the algebraic spin liquid
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Gapless edge states and their stability in two-dimensional quantum magnets
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Non-abelian bosonization in two and three spatial dimensions and applications
• Emergent Kondo behavior from gauge fluctuations in spin liquids
• Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Dual dynamic scaling in deconfined quantum criticality
• Spin-charge Separation in Nodal Antiferromagnetic Insulator
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Disturbing news about the $d=2+\epsilon$ expansion
• Fractionalized Fermi liquids and the cuprate phase diagram
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Fermionization for charge degrees of freedom and bosonization of spin degrees of freedom in the SU(2) slave-boson theory
• Spin-Peierls instability of deconfined quantum critical points
• Competing orders, the Wess-Zumino-Witten term, and spin liquids
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition
• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
• Critical structure and emergent symmetry of Dirac fermion systems
• Emergent gauge fields and their nonperturbative effects in correlated electrons
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain
• Stability of algebraic spin liquids coupled to quantum phonons
• The electromagnetic duality and the 3+1D O(6) non-linear sigma model with a level-1 Wess-Zumino-Witten term
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge
• Effects of a strict site-occupation constraint in the description of quantum spin systems at finite temperature
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model