Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin

Abstract

We use the spin functional renormalization group to investigate the $J_1$-$J_2$ quantum Heisenberg model on a square lattice. By incorporating sum rules associated with the fixed length of the spin operators as well as the nontrivial quantum dynamics implied by the spin algebra, we are able to compute the ground state phase diagram for arbitrary spin $S$, including the quantum paramagnetic phase at strong frustration. Our prediction for the extent of this paramagnetic region for $S=1/2$ agrees well with other approaches that are computationally more expensive. We find that the quantum paramagnetic phase disappears for $S\gtrsim 5$ due to the suppression of quantum fluctuations with increasing $S$.

14 pages, 4 figures

References in corpus (7)

• Exact evolution equation for the effective potential
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

Cited by in corpus (4)

• Pseudo-Majorana functional renormalization for frustrated XXZ spin-1/2 models with field or magnetization along the spin-Z direction at finite temperature
• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet
• Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice