Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study

TL;DR

This study investigates the phase diagram of the spin-1 $J_1-J_2$ Heisenberg model on a square lattice using iPEPS and DMRG methods, revealing a direct transition between Ne9el and stripe magnetic phases without an intermediate non-magnetic phase.

Contribution

The paper provides the first combined iPEPS and DMRG analysis of the spin-1 $J_1-J_2$ model, showing a direct first-order transition and absence of an intermediate phase, contrasting with the spin-1/2 case.

Findings

Identifies a direct transition at $J_2/J_1 \,\simeq 0.549$

Finds no evidence of an intermediate non-magnetic phase

Stripe order transition is first-order

Abstract

We study the spin-$1$ Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor $J_1$ and the next-nearest-neighbor $J_2$ couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the N\'eel magnetic state to the stripe magnetic state at $J_2/J_1 \simeq 0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width $L_y = 10$, we find a very small intermediate regime $\sim 0.005 J_1$ between the two magnetic order phases, which may imply the absent intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at $J_2/J_1 \simeq 0.549$. Our results indicate that unlike the spin-$1/2$ $J_1-J_2$ square model, quantum fluctuations in the spin-$1$ model may be not strong enough to stabilize an intermediate non-magnetic phase.