Neél order in square and triangular lattice Heisenberg models.

  title={Ne{\'e}l order in square and triangular lattice Heisenberg models.},
  author={Steven R. White and A L Chernyshev},
  journal={Physical review letters},
  volume={99 12},
We show that the density matrix renormalization group can be used to study magnetic ordering in two-dimensional spin models. Local quantities should be extrapolated with the truncation error, not with its square root. We introduce sequences of clusters, using cylindrical boundary conditions with pinning fields, which provide for rapidly converging finite-size scaling. We determine the magnetization for both the square and triangular Heisenberg lattices with errors comparable to the best… 

Figures from this paper

Phase diagram of the anisotropic triangular lattice Hubbard model
picture: The first type of ordering we consider is shown in Figure S2(a). Evidently, along one lattice vector the spins are ferromagnetically aligned, while along the two other bonds of the
Thermal tensor renormalization group simulations of square-lattice quantum spin models
In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite
The effects of quantum fluctuations due to frustration between nearest neighbors and next-nearest neighbors of the quantum spin-half Heisenberg antiferromagnet on a square lattice are investigated by
Spin-gap study of the model on the triangular lattice
We use the coupled cluster method implemented at high orders of approximation to study the model on the triangular lattice with Heisenberg interactions between nearest-neighbour and
Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study
Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study
Studying Two Dimensional Systems With the Density Matrix Renormalization Group
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods for studying two-dimensional quantum lattice systems, despite a perception that it is only suitable for
Low temperature properties of the triangular-lattice antiferromagnet: a bosonic spinon theory
We study the low temperature properties of the triangular-lattice Heisenberg antiferromagnet with a mean field Schwinger spin- boson scheme that reproduces quantitatively the zero temperature energy
Dynamical Structure Factor of the J1−J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields
Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current
Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
A new algorithm of quantum Monte Carlo simulations designed to detect very weak magnetic order allows high-resolution studies of the correlation between magnetic order and electrical insulation in


Long-Range Néel Order in the Triangular Heisenberg Model
We have studied the Heisenberg model on the triangular lattice using several Quantum Monte Carlo (QMC) techniques (up to 144 sites), and exact diagonalization (ED) (up to 36 sites). By studying the
Finite-size effects in Heisenberg antiferromagnets.
The precise form of the finite-size corrections is worked out, and it is claimed that the expressions so obtained will be useful for the analysis of results obtained by Monte Carlo simulations or by exact diagonalization.
Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet
We present thermodynamic measurements of various physical observables of the two dimensional S=1/2 isotropic quantum Heisenberg antiferromagnet on a square lattice, obtained by quantum Monte Carlo.
Spin-wave theory and finite-size scaling for the Heisenberg antiferromagnet.
  • WeihongHamer
  • Physics
    Physical review. B, Condensed matter
  • 1993
Spin-wave perturbation theory for the Heisenberg antiferromagnet at zero temperature is used to compute the finite-lattice corrections to the ground-state energy, the staggered magnetisation, and the
Density matrix renormalization group algorithms with a single center site
We develop a correction to the density matrix used in density matrix renormalization group calculations to take into account the incompleteness of the environment block. The correction allows
Exact spectra, spin susceptibilities, and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice.
It is shown how suitable boundary conditions, which do not frustrate N\'eel order, allow the study of samples with N=3p+1 spins, and a thorough study of these situations is done in parallel with the more conventional case N= 3p.
Density matrix formulation for quantum renormalization groups.
  • White
  • Physics
    Physical review letters
  • 1992
A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather
Density-matrix algorithms for quantum renormalization groups.
  • White
  • Physics
    Physical review. B, Condensed matter
  • 1993
A formulation of numerical real-space renormalization groups for quantum many-body problems is presented and several algorithms utilizing this formulation are outlined, which can be applied to almost any one-dimensional quantum lattice system, and can provide a wide variety of static properties.
Spin-Wave Results for the Staggered Magnetization of Triangular Heisenberg Antiferromagnet
The staggered magnetization of the Heisenberg antiferromagnet on triangular lattice is calculated by means of the usual spin-wave theory. The magnetization is derived from the ground-state energy as