Thermodynamic and spectral properties of adiabatic Peierls chains

Abstract

We present exact numerical results for the effects of thermal fluctuations on the experimentally relevant thermodynamic and spectral properties of Peierls chains. To this end, a combination of classical Monte Carlo sampling and exact diagonalization is used to study adiabatic half-filled Holstein and Su-Schrieffer-Heeger models. The classical nature of the lattice displacements in combination with parallel tempering permit simulations on large system sizes and a direct calculation of spectral functions in the frequency domain. Most notably, the long-range order and the associated Peierls gap give rise to a distinct low-temperature peak in the specific heat. The closing of the gap and suppression of order by thermal fluctuations involves in-gap excitations in the form of soliton-antisoliton pairs, and is also reflected in the dynamic density and bond structure factors as well as in the optical conductivity. We compare our data to the widely used mean-field approximation, and highlight relations to symmetry-protected topological phases and disorder problems.

Thermal and quantum lattice fluctuations in Peierls chains

“…(8). Whereas A(k, ω) has been previously studied by an exact numerical method over the entire range of temperatures for classical phonons [19] [where the bosonic part in Eq. (8) reduces to the classical result Lk B T ], the quantum case requires numerical analytic continuation and we focus on the low-temperature spectral functions characterizing the ground state.…”

“…Then, the ground state is a Peierls insulator for any λ > 0 and exactly described by mean-field theory [1,2]. The formation of a 2k F CDW is accompanied by the opening of a single-particle gap and the formation of shadow bands due to the doubling of the unit cell [19,73].…”

“…The widely used mean-field approaches [1,15] are exact for classical phonons (adiabatic limit) at T = 0. In the latter, thermal fluctuation effects (including solitons [16]) can be captured qualitatively with fluctuating gap models [17,18] and quantitatively with Monte Carlo simulations [19]. The specific heat has a characteristic peak at a temperature where coherent CDW correlations and a well-defined Peierls gap emerge [19].…”

Pseudogap crossover in the electron-phonon system

“…We study the Hamiltonian (1) in the M → ∞ limit using a Monte Carlo (MC) technique. [19][20][21] In this limit it is useful to decompose the Hamiltonian as…”

“…The partition function is classical -i.e., the phonon configurations have no time dependence -and is amenable to classical MC simulation. [19][20][21] Matrix K is Hermitian, implying that its eigenvalues are real and hence the determinant appearing in (A8) is non-negative. Therefore, there is no sign problem.…”