Ground states of quantum antiferromagnets in two dimensions

Abstract

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (Mod. Phys. Lett. B 4, 1043 (1990), http://onsager.physics.yale.edu/p32.pdf). The `minimal' model for square lattice antiferromagnets is a lattice discretization of the quantum non-linear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Neel order at weak coupling, and a confining paramagnetic ground state with bond charge (e.g. spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry group is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring non-collinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.

arXiv comment44 pages, 19 figures; SS web page: http://pantheon.yale.edu/~subir (v2) updated discussion of literature

References in corpus (30)

• An RVB phase in the triangular lattice quantum dimer model
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Quantum Criticality: competing ground states in low dimensions
• Experimental realization of a 2D fractional quantum spin liquid
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice
• Large N expansion for frustrated and doped quantum antiferromagnets
• The superconductor-insulator transition in 2D dirty boson systems
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
• Nature of the quantum phase transitions in the two-dimensional hardcore boson model
• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Dual Order Parameter for the Nodal Liquid
• The phase diagram of the hexagonal lattice quantum dimer model
• New quantum phase transitions in the two-dimensional J1-J2 model
• Quantum-Phase Transitions of Interacting Bosons and the Supersolid Phase
• Quantum Phases of the Shastry-Sutherland Antiferromagnet
• Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems
• From Neel long-range order to spin-liquids in the multiple-spin exchange model
• Exchange Frequencies in the 2d Wigner crystal
• Quantum Confinement Transition in a d-wave Superconductor
• Dual Vortex Theory of Strongly Interacting Electrons: Non-Fermi Liquid to the (Hard) Core
• Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model
• Phase transitions in the one-dimensional spin-S $J_1-J_2$ XY model
• Fractionalized Phase in an XY-Z_2 Gauge Model
• Spin-Peierls states of quantum antiferromagnets on the $Ca{V}_4{O}_9$ lattice
• Predicting the critical density of topological defects in O(N) scalar field theories

Cited by in corpus (77)

• String-net condensation: A physical mechanism for topological phases
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Order and quantum phase transitions in the cuprate superconductors
• Topological Order and Conformal Quantum Critical Points
• On the stability of U(1) spin liquids in two dimensions
• Observation of extended scattering continua characteristic of spin fractionalization in the 2D frustrated quantum magnet Cs2CuCl4 by neutron scattering
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Fermions, strings, and gauge fields in lattice spin models
• QED3 theory of underdoped high temperature superconductors
• Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
• Putting competing orders in their place near the Mott transition
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Striped phase in a quantum XY-model with ring exchange
• Quantum order from string-net condensations and origin of light and massless fermions
• A Modified Villain Formulation of Fractons and Other Exotic Theories
• Microscopic models for fractionalized phases in strongly correlated systems
• On the origin of artificial electrodynamics and other stories in three-dimensional bosonic models
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Permanent confinement in the compact QED3 with fermionic matter
• Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
• Bond order from disorder in the planar pyrochlore magnet
• Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
• Two-Dimensional Quantum XY Model with Ring Exchange and External Field
• Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Absence of U(1) spin liquids in two dimensions
• Theory of the algebraic vortex liquid in an anisotropic spin-1/2 triangular antiferromagnet
• Chirality and $Z_2$ vortices in an Heisenberg spin model on the kagomé lattice
• An Introduction to Quantum Order, String-net Condensation, and Emergence of Light and Fermions
• Kosterlitz-Thouless-like deconfinement mechanism in the 2+1 dimensional Abelian Higgs model
• Neel order, quantum spin liquids and quantum criticality in two dimensions
• 1-Dimensional behavior and sliding Luttinger liquid phase in a frustrated spin-1/2 crossed chain model: contribution of exact diagonalizations
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Higgs-confinement phase transitions with fundamental representation matter
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Understanding correlated electron systems by a classification of Mott insulators
• Geometric phases and the magnetization process in quantum antiferromagnets
• Quantum phase transitions of correlated electrons in two dimensions
• Spin density wave order, topological order, and Fermi surface reconstruction
• On the valence-bond solid phase of the crossed-chain quantum spin model
• Quantum field theory of topological spin dynamics
• Quantum phases and phase transitions of Mott insulators
• Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice
• Metal-Insulator Transition in Two- and Three-Dimensional Logarithmic Plasmas
• A chiral spin liquid wave function and the Lieb-Schulz-Mattis theorem
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
• Bond and Neel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions
• Tensor network simulation of phase diagram of frustrated J1-J2 Heisenberg model on a checkerboard lattice
• Quantum Hall spin liquids and their possible realization in moiré systems
• Confinement of matter fields in compact (2+1)-dimensional QED theory of high-$T_c$ superconductors
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Bond excitations in the pseudogap phase of the Hubbard Model
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Self-consistent theory of compact QED3 with relativistic fermions
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• A quantum phase transition from $Z_2\times Z_2$ to $Z_2$ topological order
• Tensor-product representations for string-net condensed states
• Spin solid phases of spin 1 and spin 3/2 antiferromagnets on a cubic lattice
• Bilayer Quantum Hall Ferromagnet in a Periodic Potential
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Deformed quantum double realization of the toric code and beyond
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Spin-charge separation in two dimensions: spinon-chargon gauge theories from duality
• Anisotropy-induced spin parity effects
• Phase structure of Abelian Chern-Simons gauge theories
• Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths