Projected Density of Transitions for Heisenberg Models

Yong-Cong Chen

Roger Haydock, C.M.M. Nex

Reza Haghshenas, Wang-Wei Lan, Shou-Shu Gong +1 more

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 the 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 ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$, 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 that around the same critical point the N\'eel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$. Our results indicate that unlike the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.

Roger Haydock

A method is presented for calculating binding energies and other properties of extended interacting system using the projected density of transitions (PDOT) which is the probability distribution for transitions of different energies induced by a given localized operator, the operator on which the transitions are projected. It is shown that the transition contributing to the PDOT at each energy is the one which disturbs the system least, and so, by projecting on appropriate operators, the binding energies of equilibrium electronic states and the energies of their elementary excitations can be calculated. The PDOT may be expanded as a continued fraction by the recursion method, and as in other cases the continued fraction converges exponentially with the number of arithmetic operations, independent of the size of the system, in contrast to other numerical methods for which the number of operations increases with system size to maintain a given accuracy. These properties are illustrated with a calculation of the binding energies and zone-boundary spin-wave energies for an infinite spin-$\frac{1}{2}$ Heisenberg chain, which is compared with analytic results for this system and extrapolations from finite rings of spins.

Harvey S. Leff, Michael Flicker, Kenneth Millard

J. Ginibre