Bond-order wave phase of the extended Hubbard model: Electronic solitons, paramagnetism, and coupling to Peierls and Holstein phonons

Abstract

The bond order wave (BOW) phase of the extended Hubbard model (EHM) in one dimension (1D) is characterized at intermediate correlation U = 4t by exact treatment of N -site systems. Linear coupling to lattice (Peierls) phonons and molecular (Holstein) vibrations are treated in the adiabatic approximation. The molar magnetic susceptibility χM (T ) is obtained directly up to N = 10. The goal is to find the consequences of a doubly degenerate ground state (gs) and finite magnetic gap Em in a regular array. Degenerate gs with broken inversion symmetry are constructed for finite N for a range of V near the charge density wave (CDW) boundary at V ≈ 2.18t where Em ≈ 0.5t is large. The electronic amplitude B(V ) of the BOW in the regular array is shown to mimic a tight-binding band with small effective dimerization δ ef f . Electronic spin and charge solitons are elementary excitations of the BOW phase and also resemble topological solitons with small δ ef f . Strong infrared intensity of coupled molecular vibrations in dimerized 1D systems is shown to extend to the regular BOW phase, while its temperature dependence is related to spin solitons. The Peierls instability to dimerization has novel aspects for degenerate gs and substantial Em that suppresses thermal excitations. Finite Em implies exponentially small χM (T ) at low temperature followed by an almost linear increase with T . The EHM with U = 4t is representative of intermediate correlations in quasi-1D systems such as conjugated polymers or organic ion-radical and charge-transfer salts. The vibronic and thermal properties of correlated models with BOW phases are needed to identify possible physical realizations.

Magnetic susceptibility of alkali-tetracyanoquinodimethane salts and extended Hubbard models with bond order and charge density wave phases

“…Table II, by 0.07t for the EHM and by 0.10t for PCM and EEHM. Finite-size effects are critical in view of other evidence [17,30] for broken C i symmetry in Rb-TCNQ(II), which implies V ≤ V c . By contrast, finite-size effects for the Na or K salts are absorbed in V > V c .…”

“…Low-energy excitations are accessible up to N = 16, and the full spectrum to N = 10. At constant U and t, the condition define V 1 (N ) where E σ (V ) = 0 and the degenerate gs in the BOW phase can be explicitly constructed as linear combinations of σ = ±1 functions [30]. Table I lists V s in units of t for γ = 0.2 (α M = 1.6) and U = 8t in Eq.…”

“…Their weak N dependence makes it possible to extrapolate to the extended system as discussed [36,37] in connection with a frustrated spin chain. We have computed V s (N ), V 1 (N ) and V c (N ) of all three models (EHM, EEHM, PCM) as functions of U < U * and have previously reported [30] EHM values at U = 4t.…”

“…We compute the full spectrum of H(γ) for N = 8 (10) sites with periodic (antiperiodic) boundary conditions [30]. Standard methods give the partition function Q and molar spin susceptibility χ(T ).…”

“…Subsequent studies [27][28][29] confirmed the BOW phase of the EHM and sought accurate values of V s (U ), V c (U ) and U * . We recently characterized the BOW phase of the EHM and related broken C i symmetry to electronic solitons [30]. Finite E m in regular stacks is an attractive way to rationalize χ(T ) in Fig.…”