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.