Modeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO${}_3$ and TTF-CuS${}_4$C${}_4$(CF${}_3$)${}_4$

Abstract

The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T>T_{SP}$ and mean field for $T<T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2=\alpha J_1$ between first and second neighbors, respectively, and variable frustration $0\le \alpha \le 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $\delta (T)$. The relation between $T_{SP}$ and $\Delta (\delta ,\alpha )$, the $T=0$ gap induced by dimerization, depends strongly on $\alpha$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS${}_4$C${}_4$(CF${}_3$)${}_4$ crystals ($J_1=79$ K, $\alpha =0$, $T_{SP}=12$ K) and CuGeO${}_3$ crystals ($J_1=160$ K, $\alpha =0.35$, $T_{SP}=14$ K). The same parameters describe the specific heat anomaly of CuGeO${}_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\delta (0)$ limits the range of spin correlations at $T=0$ while $T>0$ limits the range at $\delta =0$.

arXiv comment9 pages, 10 figures

References in corpus (13)

• Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• Study of the magnetic susceptibility in the spin-Peierls system CuGeO${}_3$
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• A Study of the S=1/2 Alternating Chain using Multiprecision Methods
• Reexamination of the microscopic couplings of the quasi one-dimensional antiferromagnet CuGeO_3
• Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition
• Bond-order wave phase, spin solitons and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet
• DMRG study of scaling exponents in spin-1/2 Heisenberg chains with dimerization and frustration
• Temperature Dependence of the Spin-Peierls Energy Gap and Anomalous Line Shapes in CuGeO${}_3$
• An Efficient Density Matrix Renormalization Group Algorithm for Chains with Periodic Boundary Condition
• Minimal model to describe the magnetism of $CuGe{O}_3$
• Thermodynamic Properties of the Incommensurate Phase of CuGeO_3

Cited by in corpus (6)

• Spin Peierls transition of $J_1-J_2$ and extended models with ferromagnetic $J_1$.Sublattice dimerization and thermodynamics of zigzag chains in $\beta$-TeVO${}_4$
• Low temperature thermodynamics of the antiferromagnetic $J_1-J_2$ model: Entropy, critical points and spin gap
• Density matrix renormalization group approach to the low temperature thermodynamics of correlated 1D fermionic models
• Quantum Phase Transitions in Skewed Ladder Systems
• Bond-bond correlations, gap relations and thermodynamics of spin-$1/2$ chains with spin-Peierls transitions and bond-order-wave phases
• Magnetization of electronic ground states in frustrated superstable graphs