23 research outputs found
Re-Structuring Method for the Negative Sign Problem in Quantum Spin Systems
We present detailed discussions on a new approach we proposed in a previous
paper to numerically study quantum spin systems. This method, which we will
call re-structuring method hereafter, is based on rearrangement of intermediate
states in the path integral formulation. We observed our approach brings
remarkable improvement in the negative sign problem when applied to
one-dimensional quantum spin system with next-to-nearest neighbor
interactions. In this paper we add some descriptions on our method and show
results from analyses by the exact diagonalization and by the transfer matrix
method of the system on a small chain. These results also indicate that our
method works quite effectively.Comment: 14 pages, LaTeX, figures on request, YAMANASHI-94-0
An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method
We develop a new method to calculate eigenvalues in frustrated quantum spin
models. It is based on the stochastic state selection (SSS) method, which is an
unconventional Monte Carlo technique we have investigated in recent years. We
observe that a kind of equilibrium is realized under some conditions when we
repeatedly operate a Hamiltonian and a random choice operator, which is defined
by stochastic variables in the SSS method, to a trial state. In this
equilibrium, which we call the SSS equilibrium, we can evaluate the lowest
eigenvalue of the Hamiltonian using the statistical average of the
normalization factor of the generated state.
The SSS equilibrium itself has been already observed in un-frustrated models.
Our study in this paper shows that we can also see the equilibrium in
frustrated models, with some restriction on values of a parameter introduced in
the SSS method. As a concrete example, we employ the spin-1/2 frustrated J1-J2
Heisenberg model on the square lattice. We present numerical results on the
20-, 32-, 36-site systems, which demonstrate that statistical averages of the
normalization factors reproduce the known exact eigenvalue in good precision.
Finally we apply the method to the 40-site system. Then we obtain the value
of the lowest energy eigenvalue with an error less than 0.2%.Comment: 15 pages, 12 figure
The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems
We describe a further development of the stochastic state selection method, a
new Monte Carlo method we have proposed recently to make numerical calculations
in large quantum spin systems. Making recursive use of the stochastic state
selection technique in the Lanczos approach, we estimate the ground state
energy of the spin-1/2 quantum Heisenberg antiferromagnet on a 48-site
triangular lattice. Our result for the upper bound of the ground state energy
is -0.1833 +/- 0.0003 per bond. This value, being compatible with values from
other work, indicates that our method is efficient in calculating energy
eigenvalues of frustrated quantum spin systems on large lattices.Comment: 11 page
A constrained stochastic state selection method applied to quantum spin systems
We describe a further development of the stochastic state selection method,
which is a kind of Monte Carlo method we have proposed in order to numerically
study large quantum spin systems. In the stochastic state selection method we
make a sampling which is simultaneous for many states. This feature enables us
to modify the method so that a number of given constraints are satisfied in
each sampling. In this paper we discuss this modified stochastic state
selection method that will be called the constrained stochastic state selection
method in distinction from the previously proposed one (the conventional
stochastic state selection method) in this paper. We argue that in virtue of
the constrained sampling some quantities obtained in each sampling become more
reliable, i.e. their statistical fluctuations are less than those from the
conventional stochastic state selection method. In numerical calculations of
the spin-1/2 quantum Heisenberg antiferromagnet on a 36-site triangular lattice
we explicitly show that data errors in our estimation of the ground state
energy are reduced. Then we successfully evaluate several low-lying energy
eigenvalues of the model on a 48-site lattice. Our results support that this
system can be described by the theory based on the spontaneous symmetry
breaking in the semiclassical Neel ordered antiferromagnet.Comment: 15 pgaes, 5 figure