154 research outputs found
Phase diagram of the spin-1/2 -- Heisenberg model on the square lattice
We presents the results of an extensive numerical study of the phase diagram
of the spin-1/2, \protect{--} Heisenberg model on a square
lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor
interactions , using exact diagonalization with periodic and twisted
boundary conditions. Comparison is made with published spin wave calculations.
We show that quantum fluctuations play a very important role, changing both the
extent and the wave vector of classical spiral phases, and leading to new
quantum phases where the classical spiral states have a high degeneracy. These
include a new phase with small or vanishing spin-stiffness, in addition to
known valence-bond-solid and bond-nematic phases.Comment: submitted for the International Conference on Magnetism to be held
26-31 July 2009 in Karlsruh
Quantum disorder due to singlet formation: The Plaquette lattice
I study the order/disorder transition due to singlet formation in a quantum
spin system by means of exact diagonalization. The systems is build by spin 1/2
on a two-dimensional square lattice with two different kinds of
antiferromagnetic Heisenberg interactions. The interaction J_p connects 4
nearest neighbor spins on a plaquette. The interaction J_n connects the
plaquettes with each other. If J_p=J_n the systems reduces to the simple square
lattice case. If one of the interactions becomes sufficiently larger then the
other the purely quantum effect of singlet formation drives the system into a
disordered phase with only short range correlations in the plaquettes and a
spin gap. I study the transition point by evaluating the spin gap and spin-spin
correlations. I compare the results with previously calculated data from a
non-linear sigma model approach, spin wave theory and series expansion
calculations. I confirm a critical value of J_n \approx 0.6 for the quantum
phase transition point.Comment: 5 pages (Revtex), 7 figure
Two Step Restoration of SU(2) Symmetry in a Frustrated Ring-Exchange Magnet
We demonstrate the existence of a spin-nematic, moment-free phase in a
quantum four-spin ring exchange model on the square lattice. This unusual
quantum state is created by the interplay of frustration and quantum
fluctuations which lead to a partial restoration of SU(2) symmetry when going
from a four-sublattice orthogonal biaxial Neel order to this exotic uniaxial
magnet. A further increase of frustration drives a transition to a fully gapped
SU(2) symmetric valence bond crystal.Comment: 4 pages, 5 figure
Octupolar order in the multiple spin exchange model on a triangular lattice
We show how a gapless spin liquid with hidden octupolar order arises in an
applied magnetic field, in a model applicable to thin films of 3He with
competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions.
Evidence is also presented for nematic -- i.e., quadrupolar -- correlations
bordering on ferromagnetism in the absence of a magnetic field.Comment: 4 pages, 5 figure
Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2
The frustration of antiferromagnetic interactions on the loosely connected
kagome lattice associated to the enhancement of quantum fluctuations for S=1/2
spins was acknowledged long ago as a keypoint to stabilize novel ground states
of magnetic matter. Only very recently, the model compound Herbersmithite,
ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be
synthesized and enables a close comparison to theories. We review and classify
various experimental results obtained over the past years and underline some of
the pending issues.Comment: 23 pages, 16 figures, invited paper in J. Phys. Soc. Jpn, special
topics issue on "Novel States of Matter Induced by Frustration", to be
published in Jan. 201
The incarnation of the Nersesyan-Tsvelik model in (NO)[Cu(NO3)3]
The topology of the magnetic interactions of the copper spins in the
nitrosonium nitratocuprate (NO)[Cu(NO3)3] suggests that it could be a
realization of the Nersesyan-Tsvelik model, whose ground state was argued to be
either a resonating valence bond (RVB) state or a valence bond crystal (VBC).
The measurement of thermodynamic and resonant properties reveals a behavior
inherent to low dimensional spin S = 1/2 systems and provides indeed no
evidence for the formation of long-range magnetic order down to 1.8 K.Comment: 12 pages, 6 figure
Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
In this paper, we do a complete classification of valence-bond crystals
(VBCs) on the kagome lattice based on general arguments of symmetry only and
thus identify many new VBCs for different unit cell sizes. For the spin-1/2
Heisenberg antiferromagnet, we study the relative energetics of competing
gapless spin liquids (SLs) and VBC phases within the class of
Gutzwiller-projected fermionic wave functions using variational Monte Carlo
techniques, hence implementing exactly the constraint of one fermion per site.
By using a state-of-the-art optimization method, we conclusively show that the
U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and
36-site unit cell VBCs. This stability is also preserved on addition of a
next-nearest-neighbor super-exchange coupling of both antiferromagnetic and
ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is
stabilized on addition of a very small next-nearest-neighbor FM super-exchange
coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group
symmetry as that obtained in an effective quantum dimer model study. It breaks
reflection symmetry, has a nontrivial flux pattern and is a strong dimerization
of the uniform RVB SL.Comment: 16 pages, 25 figures. Invited paper for Focus issue on "Quantum Spin
Liquids" of the New Journal of Physic
Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations
The phase diagram of a spin-1/2 model is investigated by means of
exact diagonalizations on finite samples. This model is a generalization of the
model on the square lattice with two different nearest-neighbor
couplings 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 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 which correspond
to the model.Comment: 14 pages, 21 figures, final versio
Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
We study the system size dependence of the singlet-triplet excitation gap in
the kagome-lattice Heisenberg antiferromagnet by numerical
diagonalization. We successfully obtain a new result of a cluster of 42 sites.
The two sequences of gaps of systems with even-number sites and that with
odd-number sites are separately analyzed. Careful examination clarifies that
there is no contradiction when we consider the system to be gapless.Comment: 5 pages, 3 figures, 1 table, received by J. Phys. Soc. Jpn. on 20 Jan
2011, to be published in this journa
The quantum Heisenberg antiferromagnet on the Sierpinski Gasket: An exact diagonalization study
We present an exact diagonalization study of the quantum Heisenberg
antiferromagnet on the fractal Sierpinski gasket for spin quantum numbers
s=1/2,s=1 and s=3/2. Since the fractal dimension of the Sierpinski gasket is
between one and two we compare the results with corresponding data of one- and
two-dimensional systems. By analyzing the ground-state energy, the low-lying
spectrum, the spin-spin correlation and the low-temperature thermodynamics we
find arguments, that the Heisenberg antiferromagnet on the Sierpinski gasket is
probably disordered not only in the extreme quantum case s=1/2 but also for s=1
and s=3/2. Moreover, in contrast to the one-dimensional chain we do not find a
distinct behavior between the half-integer and integer-spin Heisenberg models
on the Sierpinski gasket. We conclude that magnetic disorder may appear due to
the interplay of frustration and strong quantum fluctuations in this spin
system with spatial dimension between one and two.Comment: 12 pages (LaTeX), 7 figures, 3 tables, to appear in Physica
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