Magnetic Properties of Low-dimensional Spin-Peierls Compounds: Numerical Spectra from DMRG and Effective Field Theories

Several experiments in the last years have shown that the magnetic properties of the so-called spin-Peierls systems are well described by low-dimensional Heiseberg Hamiltonians with weak interchains coupling, an explicit dimerisation term delta and next-to-nearest neighbours interactions alpha (both in units of the exchange J). One of the most studied examples is the inorganic compound CuGeO3, because of the available quality of its crystals and of the richness of its phase diagram. In recent times, it has been shown that another inorganic compound, NaV2O5, undergoes a spin-Peierls transition at a larger temperature with respect to that of the previous system. While in this case the value of alpha is almost negligible, the dimerisation strength is about four times the one estimated for CuGeO3. As regards the energy spectrum of these systems, the elementary excitations are represented by a gapped triplet of modes which is correctly predicted by existing theoretical approaches, namely (1+1)D field theories like the double sine-Gordon and the O(3) nonlinear sigma model with nontrivial topological term. These approaches are applicable in an ample range of parameters including the regime of ferromagnetic second-neighbours interaction alpha<0. Moreover, it has been recently argued that the spectrum may contain another well-defined singlet gap, or a second stable particle in the language of relativistic quantum field theory. However, from a numerical point of view there remain some problems to investigate features like these because of the unconventional finite-size behaviour of the singlet state that converges to the thermodynamic limit in a nonmonotonic fashion. Hence, the most-commonly used method, namely exact diagonalisation, may not be sufficient even with a finite energy gap because the size at which the singlet gap exhibits a minimum can reach hundreds of sites, depending on the model's parameters. The DMRG method is a valid tool to go beyond these limits, provided that one is able to target various excited states of the spectrum in order to follow properly the singlet gap. The aim of this contribution is to discuss the field-theoretical predictions by the light of DMRG simulations of spin-Peierls Hamiltonians in a range of realistic parameters.