Emergent Potts order in the kagomé $J_1-J_3$ Heisenberg model

Abstract

Motivated by the physical properties of Vesignieite BaCu${}_3$V${}_2$O${}_8$(OH)${}_2$, we study the $J_1-J_3$ Heisenberg model on the kagomé lattice, that is proposed to describe this compound for $J_1<0$ and $J_3\gg |J_1|$. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For $J_1<0$ and $J_3>\frac{1+\sqrt{5}}{4}|J_1|$, the ground states are not all related by an Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring colinear configurations and leading to an emergent $q=4$ Potts parameter. This gives rise to a finite temperature phase transition. Effect of quantum fluctuations are studied through linear spin wave approximation and high temperature expansions of the $S=1/2$ model. For $J_3$ between $\frac{1}{4}|J_1|$ and $\frac{1+\sqrt{5}}{4}|J_1|$, the ground state goes through a succession of semi-spiral states, possibly giving rise to multiple phase transitions at low temperatures.

References in corpus (39)

• Quantum Spin Liquids
• An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice
• Vesignieite BaCu3V2O8(OH)2 as a Candidate Spin-1/2 Kagome Antiferromagnet
• The kagome antiferromagnet: a chiral topological spin liquid ?
• Lattice symmetries and regular states in classical frustrated antiferromagnets
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Scale-free antiferromagnetic fluctuations in the S=1/2 kagome antiferromagnet herbertsmithite
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Field induced transitions in a kagome antiferromagnet
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
• Frustrated two dimensional quantum magnets
• Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System
• Magnetic phase diagrams of classical triangular and kagome antiferromagnets
• Dzyaloshinsky-Moriya interaction in vesignieite: A route to freezing in a quantum kagome antiferromagnet
• Magnetization Plateaus in the Spin-1/2 Kagome Antiferromagnets: Volborthite and Vesignieite
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Ground State and Intrinsic Susceptibility of the Kagome Antiferromagnet Vesignieite as seen by 51V NMR
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Phase transition in a 2-dimensional Heisenberg model
• Spin dynamics in the S =1/2 kagome compound vesignieite, Cu3Ba(VO5H)2
• Vesignieite: a $S=\frac{1}{2}$ kagome antiferromagnet with dominant third-neighbor exchange
• Chirality and $Z_2$ vortices in an Heisenberg spin model on the kagomé lattice
• Spin susceptibility of quantum magnets from high to low temperatures
• Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures
• Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice
• Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach
• Spin-1/2 kagome compounds: volborthite vs herbertsmithite
• Strong quantum effects in an almost classical antiferromagnet on a kagome lattice
• Broken translational symmetry in an emergent paramagnetic phase of graphene
• Fictitious excitations in the classical Heisenberg antiferromagnet on the kagome lattice
• Anticollinear magnetic order induced by impurities in the frustrated Heisenberg model of pnictides
• Parallel-tempering cluster algorithm for computer simulations of critical phenomena
• Canted Antiferromagnetic Order in the Kagome Material Sr-Vesignieite
• Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

Cited by in corpus (19)

• Pinch-points to half-moons and up in the stars: the kagome skymap
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• Emergent skyrmion-based chiral order in zero-field Heisenberg antiferromagnets on the breathing kagome lattice
• Competing emergent Potts orders and possible nematic spin liquids in the Kagome $J_1-J_3$ Heisenberg model
• Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet
• Classical ground states of spin lattices
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
• Zero-field miniature skyrmion crystal and chiral domain state in breathing-kagome antiferromagnets
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Chiral order emergence driven by quenched disorder
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
• Stripe order in quasicrystals
• The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
• Robust semiclassical magnetization plateau in the kagome lattice