Abstract
We study, on the basis of the general entangled-plaquette variational ansatz, the ground-state (GS) properties of the spin- antiferromagnetic Heisenberg model on the triangular lattice. Our numerical estimates are in good agreement with available exact results and comparable, for large system sizes, to those computed via the best alternative numerical approaches, or by means of variational schemes based on specific (i.e. incorporating problem-dependent terms) trial wave functions (WFs). The extrapolation to the thermodynamic limit of our results for lattices comprising up to N=324 spins yields an upper bound of the GS energy per site (in units of the exchange coupling) of − 0.5458(2) [−0.4074(1) for the XX model], while the estimated infinite-lattice order parameter is 0.3178(5) (i.e. ∼64% of the classical value).
Highlights
In the last decades quantum Monte Carlo (QMC) [1] has emerged as one of the most powerful numerical tools to study the ground-state (GS) properties of quantum spin systems on a lattice
A variety of variational ansatze, as illustrated in [25], have a straigthforward representation in terms of entangled-plaquette states (EPS). This is, for example, the case of the wave function (WF) introduced by Huse and Elser [27] for the antiferromagnetic Heisenberg model (AHM) on the triangular lattice which contains up to three-spin correlations and a phase factor that depends on the system geometry
We show results obtained with EPS for the 2D AHM on the triangular lattice
Summary
In the last decades quantum Monte Carlo (QMC) [1] has emerged as one of the most powerful numerical tools to study the ground-state (GS) properties of quantum spin systems on a lattice. Projected-entangled pair states (PEPS) [5], the natural extension to higher spatial dimensions of the matrix product states variational family, which constitutes the foundation of DMRG, can efficiently approximate GS’s of local Hamiltonians [6], and have been successfully employed to simulate frustrated and bipartite quantum spin systems [7, 8, 9, 10, 11] Their applicability, is restricted by the disadvantageous scaling of the computational cost to 2D models with open boundary conditions.
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