Finite temperature density-matrix-renormalization-group investigation of the spin-Peierls transition inCuGeO3

Abstract

We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO 3 . A variant of the finite temperature density matrix renormalization group ͑DMRG͒ allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO 3 such as magnetic dimerization, critical temperature, susceptibility, and entropy.

Pressure dependence and non-universal effects of microscopic couplings on the spin-Peierls transition in CuGeO

“…With respect to this, the recently developed transfer matrix DMRG (TMRG) [9][10][11] on the basis of transfer matrices [12] provides a very powerful method to calculate thermodynamic quantities of spin chains without any use of perturbative methods. This has been demonstrated in several applications [4,11,[13][14][15][16][17].…”

“…3. Using the scaling of A [4], the definition of the critical temperature and the dependence of the ground state energy on small saturation dimerizations δ 0 = δ(T = 0) one finds…”

“…For applications to CuGeO 3 it is furthermore uncertain if the pure Heisenberg chain can even yield the qualitative results correctly. From the analysis of the susceptibility data at higher temperature we are led to favour the frustration parameter α = 0.35 [2][3][4] for which the behaviour of the response function deviates considerably from χ 0 /x.…”

“…The divergence of A(x) for free fermions, Heisenberg model with α < α c , α = α c , and α > α c , is log(x), 1/x × log. corrections [4,27], 1/x (see [22] and references therein), and exponential [4], respectively. The quantitative values for x SP · A(x SP ) also differ from each other.…”

“…In the dimerized phase, many features were shown to be consistent within an adiabatic description of the phonon degrees of freedom. This observation comprises zero temperature [5][6][7][8] as well as thermodynamic properties [4].…”