22 research outputs found

### Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model

We combine the Density Matrix Technique (DMRG) with Green Function Monte
Carlo (GFMC) simulations. The DMRG is most successful in 1-dimensional systems
and can only be extended to 2-dimensional systems for strips of limited width.
GFMC is not restricted to low dimensions but is limited by the efficiency of
the sampling. This limitation is crucial when the system exhibits a so-called
sign problem, which on the other hand is not a particular obstacle for the
DMRG. We show how to combine the virtues of both methods by using a DMRG
wavefunction as guiding wave function for the GFMC. This requires a special
representation of the DMRG wavefunction to make the simulations possible within
reasonable computational time. As a test case we apply the method to the
2-dimensional frustrated Heisenberg antiferromagnet. By supplementing the
branching in GFMC with Stochastic Reconfiguration (SR) we get a stable
simulation with a small variance also in the region where the fluctuations due
to minus sign problem are maximal. The sensitivity of the results to the choice
of the guiding wavefunction is extensively investigated. We analyse the model
as a function of the ratio of the next-nearest to nearest neighbor coupling
strength. We observe in the frustrated regime a pattern of the spin
correlations which is in-between dimerlike and plaquette type ordering, states
that have recently been suggested. It is a state with strong dimerization in
one direction and weaker dimerization in the perpendicular direction.Comment: slightly revised version with added reference

### Spin Stiffness in the Hubbard model

The spin stiffness $\rho_{\rm s}$ of the repulsive Hubbard model that occurs
in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the
same as the thermodynamically defined stiffness involved in twisting the order
parameter. New expressions for $\rho_{\rm s}$ are derived, which enable easier
interpretation, and connections with superconducting weight and gauge
invariance are discussed.Comment: 21 Pages LaTeX2e, to be published in Journal of Physics

### The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation

We have adjusted the Density Matrix Renormalization method to handle two
dimensional systems of limited width. The key ingredient for this extension is
the incorporation of symmetries in the method. The advantage of our approach is
that we can force certain symmetry properties to the resulting ground state
wave function. Combining the results obtained for system sizes up-to $30 \times
6$ and finite size scaling, we derive the phase transition point and the
critical exponent for the gap in the Ising model in a Transverse Field on a two
dimensional square lattice.Comment: 9 pages, 8 figure

### A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

It has proved difficult to extend the density matrix renormalization group
technique to large two-dimensional systems. In this Communication I present a
novel approach where the calculation is done directly in two dimensions. This
makes it possible to use an infinite system method, and for the first time the
fixed point in two dimensions is studied. By analyzing several related blocking
schemes I find that there exists an algorithm for which the local energy
decreases monotonically as the system size increases, thereby showing the
potential feasibility of this method.Comment: 5 pages, 6 figure

### Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the
spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility
associated to the breaking of the translational invariance are calculated for
the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when
compared to the one dimensional case, where the occurrence of a dimerized phase
for large enough frustration is well established -- suggest either a
homogeneous spin liquid or, possibly, a dimerized state with a rather small
order parameter

### The Heisenberg model on the 1/5-depleted square lattice and the CaV4O9 compound

We investigate the ground state structure of the Heisenberg model on the
1/5-depleted square lattice for arbitrary values of the first- and
second-neighbor exchange couplings. By using a mean-field Schwinger-boson
approach we present a unified description of the rich ground-state diagram,
which include the plaquette and dimer resonant-valence-bond phases, an
incommensurate phase and other magnetic orders with complex magnetic unit
cells. We also discuss some implications of ours results for the experimental
realization of this model in the CaV4O9 compound.Comment: 4 pages, Latex, 7 figures included as eps file

### Phase Diagram of the Spin-Orbital model on the Square Lattice

We study the phase diagram of the spin-orbital model in both the weak and
strong limits of the quartic spin-orbital exchange interaction. This allows us
to study quantum phase transitions in the model and to approach from both sides
the most interesting intermediate-coupling regime and in particular the
SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al
[Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of
the system is a plaquette spin-orbital liquid. We argue that the state is more
complex. There is plaquette order, but it is anisotropic: bonds in one
direction are stronger than those in the perpendicular direction. This order is
somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg
spin model.Comment: 8 pages, 4 Postscript figure

### Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet

We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.Comment: 7 pages, 11 figures, RevTeX minor changes made, Figure 6 correcte

### Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of
exact diagonalizations on finite samples. This model is a generalization of the
$J_1-J_2$ model on the square lattice with two different nearest-neighbor
couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg
chains. The results suggest that the resonnating valence bond state predicted
by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J'
\ll J$ is realized and extends beyond the limit of small interchain coupling
along a curve nearly coincident with the line where the energy per spin is
maximum. This line is likely bordered on both side by a columnar dimer long
range order. This columnar order could extends for $J'\to J$ which correspond
to the $J_1-J_2$ model.Comment: 14 pages, 21 figures, final versio