Christian Knetter

Dispersion and symmetry of bound states in the shastry-sutherland model

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)(14)] permit one to fix the parameters of SrCu2(BO3)(2) precisely: J1 = 6.16(10) meV, x J2/J1 = 0.603(3), J( perpendicular) = 1.3(2) meV. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x = 0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.

Perturbation theory by flow equations : dimerized and frustrated S = 1/2 chain

Abstract:The flow equation method (Wegner, 1994) is used as continuous unitary transformation to construct perturbatively effective Hamiltonians. The method is illustrated in detail for dimerized and frustrated antiferromagnetic S=1/2 chains. The effective Hamiltonians conserve the number of elementary excitations which are S=1 magnons for the dimerized chains. The sectors of different number of excitations are clearly separated. Easy-to-use results for the gap, the dispersion and the ground state energies of the chains are provided.

Observation of Two-Magnon Bound States in the Two-Leg Ladders of (Ca, La)14Cu24O41

Phonon-assisted two-magnon absorption is studied in the spin- 1/2 two-leg ladders of (Ca,La)(14)Cu(24)O(41) for E parallel c (legs) and E parallel a (rungs). We verify the theoretically predicted existence of two-magnon singlet bound states, which give rise to peaks at approximately equal to 2140 and 2800 cm(-1). The two-magnon continuum is observed at approximately equal to 4000 cm(-1). Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for J parallel approximately equal to 1020-1100 cm(-1), J parallel/J perpendicular approximately equal to 1-1.2. At high energies, the magnetic contribution to sigma(omega) is strikingly similar in the ladders and in the undoped high-T(c) cuprates, which emphasizes the importance of strong quantum fluctuations in the latter.

Exact demonstration of magnetization plateaus and first-order dimer-Neel phase transitions in a modified shastry-sutherland model for SrCu2(BO3)(2)

We study a generalized Shastry-Sutherland model for the material SrCu2(BO3)(2). Along a line in the parameter space, we show rigorously that the model has a first-order phase transition between dimerized and Neel-ordered ground states. Furthermore, when a magnetic field is applied in the dimerized phase, magnetization plateaus develop at commensurate values of the magnetization. We also discuss various aspects of the phase diagram and properties of this model away from this exactly soluble line, which include gap-closing continuous transitions between dimerized and magnetically ordered phases.

Raman response in antiferromagnetic two-leg S = 1/2 Heisenberg ladders

The Raman response in the antiferromagnetic 2-leg S = 1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV2O5 and La y Ca 14 − y Cu24O41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.

The structure of operators in effective particle-conserving models

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables. The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details on how to implement the approach perturbatively for a large class of systems are presented.

High order perturbation theory for spectral densities of multi-particle excitations: \(\mathsf{S = \frac{1}{2}}\) two-leg Heisenberg ladder

Abstract.We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous unitary transformation introduced previously. It is conceived to work particularly well in models allowing a clear identification of the elementary excitations above the ground state. These are then viewed as quasi-particles above the vacuum. The article focuses on the technical aspects and includes a discussion of series extrapolation schemes. The strength of the method is demonstrated for S = 1/2 two-leg Heisenberg ladders, for which results are presented.

Dynamic structure factor of the two-dimensional Shastry-Sutherland model.

We calculate the two-triplon contribution to the dynamic structure factor of the two-dimensional Shastry-Sutherland model, realized in SrCu2(BO3)(2), by means of perturbative continuous unitary transformations. For realistic parameters we find flat bound two-triplon bands. These bands show large weight in the structure factor depending strongly on momentum. So our findings permit a quantitative understanding of high precision inelastic neutron scattering experiments.

Symmetries and triplet dispersion in a modified Shastry-Sutherland model for SrCu2(BO3)2

We investigate the one-triplet dispersion in a modified Shastry-Sutherland model for SrCu2(BO3)2 by means of a series expansion about the limit of strong dimerization. Our perturbative method is based on a continuous unitary transformation that maps the original Hamiltonian to an effective, energy-quanta-conserving block diagonal Hamiltonian eff. The dispersion splits into two branches which are nearly degenerate. We analyse the symmetries of the model and show that space group operations are necessary to explain the degeneracy of the dispersion at k = 0 and at the border of the magnetic Brillouin zone. Moreover, we investigate the behaviour of the dispersion for small |k| and compare our results to inelastic neutron scattering data.

Charge-order-induced sharp Raman peak in Sr14Cu24O41.

In the two-leg S=1/2 ladders of Sr14Cu24O41, a modulation of the exchange coupling arises from the charge order within the other structural element, the CuO2 chains. In general, breaking transla-tional invariance by modulation causes gaps within the dispersion of elementary excitations. We show that the gap induced by the charge order can drastically change the magnetic Raman spectrum, leading to the sharp peak observed in Sr14Cu24O41. This sharp Raman line gives insight into the charge-order periodicity and hence into the distribution of carriers. The much broader spectrum of La6Ca8Cu24O41 reflects the response of an undoped ladder in the absence of charge order.