caron@physique.usherb.ca
to communicate with me.In 1993, I wrote a review article on the theory of organic conductors which focussed on the developments, over the last 15 years, in the areas of electronic correlations and electron-phonon coupling. It covered, sometimes in a new perspective, on the diversity of the physical properties of contemporary quasi-one-dimensional solids: solitons, magnetism, Peierls and spin-Peierls transitions, superconductivity, disorder.
L.G. Caron, Basic Physical Concepts of Organic Conductors, in "Organic Conductors, fundamentals and applications", J.-P. Farges ed., Vol. 4 in the series "Applied Physics", A.M. Hermann ed. (Dekker, New York, 1994), P. 25-73.
I got introduced to the density matrix renormalization group (DMRG) method ,developed by S. White at UCI , while spending some time at UCSB. This method was just being applied to the half-filled Kondo lattice, a problem which had been taking a lot of my energies. The method showed such precision in ground state calculations of one-dimensional (1D) systems that I decided not to further court the quantum Monte Carlo method. When I got back to Sherbrooke, I decided to initiate a research program on the method with the recently arrived post-doc S. Moukouri. We decided on undertaking a simple problem, the Kondo necklace, which involved a limited spin-space dimension per site. This problem was also close enough to the Kondo lattice to be of interest. It took a year or so to get properly functioning algorithms. We were able to calculate the spin gap and show that a predicted Kosterlitz-Thouless transition did not occur. We also concluded that this model was in the same universality class as the Kondo lattice. We then went on to calculate models with itinerant electrons like the t-J-Kondo lattice and the non half-filled Kondo lattice. These calculations allowed us to verify many predictions that had been made using other techniques, the importance of self-screening of the local spins or the ferromagnetic state of the partially filled lattices at large coupling for instance..
S. Moukouri, L.G. Caron, C. Bourbonnais, and L. Hubert, Real-space density matrix renormalization-group study of the Kondo necklace, Phys. Rev. B 51, 15920-24 (1995).
S. Moukouri and L.G. Caron, Ground-state properties of the one-dimensional Kondo lattice at partial band filling, Phys. Rev. B 52, R15723-26 (1995).
S. Moukouri, Liang Chen, and L.G. Caron, Local moments coupled to a strongly correlated electron chain, Phys. Rev. B 53, R488-491 (1996).
This last work, however, also put us on the trail of another problem pertaining to the size of the Fermi surface in heavy-fermion metals and also, as it turns out, in these 1D conducting chains. The evidence for a large Fermi surface was not convincing, however. We thus turned back to the Kondo lattice at partial filling and found a range of parameters for which the large Fermi surface could be convincingly observed.
S. Moukouri and L.G. Caron, Fermi Surface of the One-dimensional Kondo Lattice Model, Phys. Rev. B. 54, 12212-12215 (1996).
While this was going on, I had been talking of the method with colleagues which mentioned that it might be interesting if the DMRG might be applied to phonons. The immediate foreseeable difficulty was the infinite dimensional space associated with phonons which would have to be truncated and at what cost? I was quickly reassured when I could show that the number of virtual phonons at any lattice site could be reasonably small in 1D Peierls or spin-Peierls ground-states. I then decided to do simulations on the XY spin-Peierls problem coupled to dispersionless inter-molecular vibrations. This involved a minimal spin-space on a site. In this problem, the spins can be mapped into non-interaction spinless fermions. The hope was to keep the truncated vibration space within a manageable size. We were able to do this using the infinite chain algorithm and to map out the ground-state phase diagram as a function of the phonon frequency and the strength of the spin-phonon coupling. We found considerable quantum renormalization of the spin gap due to finite phonon frequency. We also confirmed the Kosterlitz-Thouless transition to a gapless quantum regime for sufficiently small coupling. I am at present finishing a study of the ground state of acoustic phonons having full dispersion. The problem with this is twofold. First the presence of hydrodynamic modes produces logarithmically increasing vibration amplitudes, and thus of virtual phonons, as chain lengths increase. This makes the infinite chain algorithm of finite interest because of the truncation of the phonon space which limits the vibrational amplitude to small values and because the "fixed point" is constantly changing. Second, using the exact phonon modes (in momentum space) translates into a long-range inter-molecular coupling when doing numerical calculations in real space; this creates a problem of accuracy in the DMRG.
L.G. Caron and S. Moukouri, Density Matrix Renormalization Group Applied to the Ground State of the XY Spin-Peierls System, Phys. Rev. Lett. 76, 4050-4053 (1996).
One other major preoccupation of the DMRG from the start was with its generalization to finite temperatures (thermodynamic DMRG). White had done the preliminary ground breaking on this aspect of his method. The potential seemed great and, presumably, one might achieve better accuracy than the quantum Monte Carlo method (also without the sign problems plaguing this method). We toiled for three years on this problem, trying to find a satisfactory criterion for the "goodness" of the thermodynamic calculations, We finally developed a new procedure which was tried on a Heisenberg spin-one-half chain, for which there are exact Bethe ansatz results. The results were fine down to appreciably low temperatures: T==0.05J.
S. Moukouri and L.G. Caron, Thermodynamic Density Matrix Renormalization Group Study of the Magnetic Susceptibility of Half-Integer Quantum Spin Chains, Phys. Rev. Lett. 77, 4640-4643 (1996).
This project is the object of the Ph.D. thesis of A. Sedeki. It is a follow up on the previous attempt at understanding the Kondo lattice using the RG [L.G. Caron et C. Bourbonnais Renormalization in the one-dimensional Kondo lattice: the Nozières criterion. Europhys. Lett. 11, 473-78 (1990)]. We propose to expand the parameter space of the pristine Kondo lattice to include RG generated interactions (that are not in the pristine Hamiltonian) as has been shown to occur in quasi-1D conductors.
L.G. Caron, S. Robillard, G. Vachon, J. Gauthier, M. Michaud et L. Sanche, Anisotropic cross sections in low-energy electron reflection spectroscopy on solids, Phys. Rev. B 43, 2347-2354 (1991).
P. Andry, A.Y. Filion, S. Blain, A. Rambo, and L.G. Caron, Inversion induced in silicon by corona-charged PVDF, P(VDF/TriFE), and VDF/ClTriFE), J. Appl. Phys. 69, 2644-2655 (1991).
J. Lefebvre, J. Beerens, C. Bourbonnais, L.G. Caron, C. Lenoir et P. Batail, Gap determination in the Field-Induced-Spin-Density-Wave State of (TMTSF)2ClO4 via Far-Infrared Photoconductivity, Phys. Rev. Lett. 72, 3417-20 (1994).
L. Pan, L.G. Caron, R. Loucif-Saïbi, D. Houde, Thu-Hoa Tran-Thi, and Lê Dao, Time-Resolved Four-Wave Mixing Study on Sublimated Films of Cerium Porphyrin Phthalocyanine Heterodimer System, Phys. Rev. B.
C. Bourbonnais and L.G. Caron, Renormalization group approach to quasi-one-dimensional conductors, Int. J. Mod. Phys. B 6&7, 1033-1096 (1991), also appeared in The Hubbard Model, Series on Advances in Statistical Mechanics, Vol. 7, (World Scientific, 1991).
Click here to come back to the cover page..
Last update, Laurent Caron, 6 january 1997
caron@physique.usherb.ca
to communicate with me.