Lattice dynamical effects on the peierls transition in one-dimensional metals and spin chains

Abstract

Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless buttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green's function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3.

Spectral signatures of the Luttinger liquid to the charge-density-wave transition

“…4 The halffilled HMSF captures the relevant physics of the more general quarter-filled Hubbard-Holstein model 3,4 in the regime of large Hubbard repulsion U ≫ t, often realized in experiment, where on-site bipolaron formation is suppressed. 2,9). In the adiabatic limit ω0 → 0 the critical dimensionless coupling constant λc converges to zero.…”

“…At present the probably most precise phase boundary is obtained by exact diagonalization and density matrix renormalization group (DMRG) techniques. 2,9 More recent large-scale DMRG calculations supplemented by a finite-size analysis have proved that at low (high) phonon frequencies the metallic LL phase is characterised by an attractive (repulsive) interaction. 10 But also above g c (ω 0 ), where long-range CDW order sets in, there exist two physically distinct regimes, which can be classified, e.g., by their different optical response, 9 either as a band insulator in the adiabatic regime ω 0 /t ≪ 1 or as a polaronic superlattice in the limit of large phonon frequencies ω 0 /t ≫ 1 (see Fig.…”

Spin-phonon chains with bond coupling

“…which is frequently used 8,10,13,15,25 , especially in connection with CuGeO 3 . For this type of coupling single harmonic degrees of freedom directly modify the magnetic interaction.…”

Nature of the Peierls- to Mott-insulator transition in 1D

“…A controversial issue is the nature of the PI-MI transition and whether or not only one quantum critical point separates the PI and MI phases in purely electronic model Hamiltonians [1,2,3,4,5]. Phonon dynamical effects, which are known to be particularly important in low-dimensional materials [6,7] may further modify the transition.…”