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Using examples of the square- and triangular-lattice Heisenberg models we demonstrate that the density matrix renormalization group method (DMRG) can be effectively used to study magnetic ordering in two-dimensional lattice spin models.
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These QMC calculations predate the loop algorithm improvements, but include detailed information on scaling behavior from chiral perturbation theory
Cited in the paper.
In practice, one measures ε \varepsilon relative to an approximate state, and at best ε ∝ | Δ ψ | 2 \varepsilon\propto|\Delta\psi|^{2} , as m m is increased. This proportionality, which makes an extrapolation possible, is usually observed if the system and environment blocks both have m m states, and if the energy is well-converged for this value of m m
Cited in the paper.
Central site operators also have a polynomial dependence on the error in the total energy, providing an alternative extrapolation method, based on a separate extrapolation of the energy
Cited in the paper.
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Simulations were performed using the stochastic series algorithm in the ALPS library, http://alps.comp-phys.org/. See F. Alet, S. Wessel and M. Troyer, Phys. Rev. E 71
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