2,090 research outputs found
High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with
The coupled cluster method (CCM) is a powerful and widely applied technique
of modern-day quantum many-body theory. It has been used with great success in
order to understand the properties of quantum magnets at zero temperature. This
is due largely to the application of computational techniques that allow the
method to be applied to high orders of approximation using localised
approximation schemes, e.g., such as the LSUB scheme. In this article, the
high-order CCM formalism for the ground and excited states of quantum magnetic
systems are extended to those with spin quantum number .
Solution strategies for the ket- and bra-state equations are also considered.
Aspects of extrapolation of CCM expectation values are discussed and future
topics regarding extrapolations are presented.Comment: 15 page
Density Matrix Renormalisation Group Calculations for Two-Dimensional Lattices: An Application to the Spin-Half and Spin-One Square-Lattice Heisenberg Models
A new density matrix renormalisation group (DMRG) approach is presented for
quantum systems of two spatial dimensions. In particular, it is shown that it
is possible to create a multi-chain-type 2D DMRG approach which utilises
previously determined system and environment blocks {\it at all points}. One
firstly builds up effective quasi-1D system and environment blocks of width
and these quasi-1D blocks are then used to as the initial building-blocks of a
new 2D infinite-lattice algorithm. This algorithm is found to be competitive
with those results of previous 2D DMRG algorithms and also of the best of other
approximate methods. An illustration of this is given for the spin-half and
spin-one Heisenberg models on the square lattice. The best results for the
ground-state energies per bond of the spin-half and spin-one square-lattice
Heisenberg antiferromagnets for the lattice using this
treatment are given by and ,
respectively.Comment: 7 Figures. Accepted for publication in Phys. Rev.
The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
We investigate the ground-state magnetic order of the spin-1/2 J1-J2
Heisenberg model on the square lattice with ferromagnetic nearest-neighbor
exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange
J2>0. We use the coupled-cluster method to high orders of approximation and
Lanczos exact diagonalization of finite lattices of up to N=40 sites in order
to calculate the ground-state energy, the spin-spin correlation functions, and
the magnetic order parameter. We find that the transition point at which the
ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1| (exact
diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our
results for ferromagnetic J1 with established results for the spin-1/2 J1-J2
Heisenberg model with antiferromagnetic J1. We find that both models (i.e.,
ferro- and antiferromagnetic J1) behave similarly for large J2, although
significant differences between them are observed for J2/|J1| \lesssim 0.6.
Although the semiclassical collinear magnetic long-range order breaks down at
J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar
breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model
with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an
intermediate disordered phase does occur between the phases exhibiting
semiclassical collinear stripe order and ferromagnetic order for ferromagnetic
J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.Comment: 15 pages, 7 figures, 2 table
Ab Initio Calculations of the Spin-Half XY Model
In this article, the correlated basis-function (CBF) method is applied for
the first time to the quantum spin-half {\it XY} model on the linear chain, the
square lattice, and the simple cubic lattice. In this treatment of the quantum
spin-half {\it XY} model a Jastrow ansatz is utilised to approximate the
ground-state wave function. Results for the ground-state energy and the
sublattice magnetisation are presented, and evidence that the CBF detects the
quantum phase transition point in this model is also presented. The CBF results
are compared to previous coupled cluster method (CCM) results for the spin-half
{\it XY} model, and the two formalisms are then compared and contrasted.Comment: 10 pages, 3 figure
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