77 research outputs found
Exact ground state and kink-like excitations of a two dimensional Heisenberg antiferromagnet
A rare example of a two dimensional Heisenberg model with an exact dimerized
ground state is presented. This model, which can be regarded as a variation on
the kagome lattice, has several features of interest: it has a highly (but not
macroscopically) degenerate ground state; it is closely related to spin chains
studied by earlier authors; in particular, it is probably the first genuinely
two-dimensional quantum system to exhibit domain-wall-like ``kink'' excitations
normally found only in one-dimensional systems. In some limits it decouples
into non-interacting chains, purely dynamically and not because of weakening of
interchain couplings: indeed, paradoxically, this happens in the limit of
strong coupling of the chains.Comment: 4 pages, revtex, 5 figures included via epsfi
Quantum Entanglement in Heisenberg Antiferromagnets
Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is
investigated using the concurrence measure. For a nondegenerate S=0 ground
state, a simple formula relates the concurrence to the diagonal correlation
function. The concurrence length is seen to be extremely short. A few finite
clusters are studied numerically, to see the trend in higher dimensions. It is
argued that nearest-neighbour concurrence is zero for triangular and Kagome
lattices. The concurrences in the maximal-spin states are explicitly
calculated, where the concurrence averaged over all pairs is larger than the
S=0 states.Comment: 7 pages, 3 figure
Crossover behavior of the J1-J2 model in a staggered magnetic field
The ground states of the Heisenberg chain with the
nearest-neighbor and the next-nearest-neighbor antiferromagnetic couplings are
numerically investigated in a staggered magnetic field. While the staggered
magnetic field may induce the N\'eel-type excitation gap, and it is
characterized by the Gaussian fixed point in the spin-fluid region, the
crossover to the behavior controlled by the Ising fixed point is expected to be
observed for the spontaneously dimerized state at finite field. Treating a
low-lying excitation gap by the phenomenological renormalization-group method,
we numerically determine the massless flow connecting the Gaussian and Ising
fixed points. Further, to check the criticalities, we perform the
finite-size-scaling analysis of the excitation gap.Comment: 4 pages, 3 figure
Series study of the One-dimensional S-T Spin-Orbital Model
We use perturbative series expansions about a staggered dimerized ground
state to compute the ground state energy, triplet excitation spectra and
spectral weight for a one-dimensional model in which each site has an S=\case
1/2 spin and a pseudospin , representing a doubly
degenerate orbital. An explicit dimerization is introduced to allow study of
the confinement of spinon excitations. The elementary triplet represents a
bound state of two spinons, and is stable over much of the Brillouine zone. A
special line is found in the gapped spin-liquid phase, on which the triplet
excitation is dispersionless. The formation of triplet bound states is also
investigated.Comment: 9 pages, 9 figure
Lieb-Schultz-Mattis in Higher Dimensions
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional
spin systems is shown. The physical motivation for the result is that such spin
systems typically either have long-range order, in which case there are gapless
modes, or have only short-range correlations, in which case there are
topological excitations. The result uses a set of loop operators, analogous to
those used in gauge theories, defined in terms of the spin operators of the
theory. We also obtain various cluster bounds on expectation values for gapped
systems. These bounds are used, under the assumption of a gap, to rule out the
first case of long-range order, after which we show the existence of a
topological excitation. Compared to the ground state, the topologically excited
state has, up to a small error, the same expectation values for all operators
acting within any local region, but it has a different momentum.Comment: 14 pages, 3 figures, final version in pres
Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
As a simple model for spin-Peierls systems we study a frustrated Heisenberg
chain coupled to optical phonons. In view of the anorganic spin-Peierls
compound CuGeO3 we consider two different mechanisms of spin-phonon coupling.
Combining variational concepts in the adiabatic regime and perturbation theory
in the anti-adiabatic regime we derive effective spin Hamiltonians which cover
the dynamical effect of phonons in an approximate way. Ground-state phase
diagrams of these models are determined, and the effect of frustration is
discussed. Comparing the properties of the ground state and of low-lying
excitations with exact diagonalization data for the full quantum spin phonon
models, good agreement is found especially in the anti-adiabatic regime.Comment: 9 pages, 7 figures included, submitted to Phys. Rev.
Exact Groundstates for Antiferromagnetic Spin-One Chains with Nearest and Next-Nearest Neighbour Interactions
We have found the exact ground state for a large class of antiferromagnetic
spin-one chains with nearest and next-nearest neighbour interactions. The
ground state is characterized as a matrix product of local site states and has
the properties characteristic of the Haldane scenario.Comment: 8 pages, to appear in Z. Phys. B, preprint Cologne-94-474
A new family of matrix product states with Dzyaloshinski-Moriya interactions
We define a new family of matrix product states which are exact ground states
of spin 1/2 Hamiltonians on one dimensional lattices. This class of
Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but
at specified and not arbitrary couplings. We also compute in closed forms the
one and two-point functions and the explicit form of the ground state. The
degeneracy structure of the ground state is also discussed.Comment: 15 pages, 1 figur
Exactly solvable model of three interacting particles in an external magnetic field
The quantum mechanical problem of three identical particles, moving in a
plane and interacting pairwise via a spring potential, is solved exactly in the
presence of a magnetic field. Calculations of the pair--correlation function,
mean distance and the cluster area show a quantization of these parameters.
Especially the pair-correlation function exhibits a certain number of maxima
given by a quantum number. We obtain Jastrow pre-factors which lead to an
exchange correlation hole of liquid type, even in the presence of the
attractive interaction between the identical electrons.Comment: 8 pages 3 figure
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