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arXiv:1605.02779 · Physical review. B./Physical review. B

Thermodynamic and spectral properties of adiabatic Peierls chains

Manuel Weber, Fakher F. Assaad, Martin Hohenadler

Published Oct 28, 2016• 11 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevb.94.155150

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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.
Thermodynamic and spectral properties of electrons coupled to quantum phonons are studied in the framework of the one-dimensional spinless Holstein model. Using quantum Monte Carlo simulations and an efficient exact estimator for the specific heat based on the properties of the perturbation expansion we calculate the specific heat and compressibility for the entire range of electron-phonon couplings and phonon frequencies. Our results reveal how the Peierls gap and long-range order at zero temperature as well as the significant renormalization of electrons and phonons---revealed by the corresponding spectral functions---manifest themselves in the specific heat. We also quantitatively assess the validity for the widely used classical phonon approximation and identify the electronic contribution predicted for a Tomonaga-Luttinger liquid.
We use the continuous-time interaction expansion (CT-INT) quantum Monte Carlo method to calculate the phonon spectral function of the one-dimensional Holstein-Hubbard model at half-filling. Our results are consistent with a soft-mode Peierls transition in the adiabatic regime, and the existence of a central peak related to long-range order in the Peierls phase. We explain a previously observed feature at small momenta in terms of a hybridization of charge and phonon excitations. Tuning the system from a Peierls to a metallic phase with a nonzero Hubbard interaction suppresses the central peak, but a significant renormalization of the phonon dispersion remains. In contrast, the dispersion is only weakly modified in the Mott phase. We discuss finite-size effects, the relation to the dynamic charge structure factor, as well as additional sum rules and their implications. Finally, we reveal the existence of a discrete symmetry in a continuum field theory of the Holstein model, which is spontaneously broken in the Peierls phase.
We analyze several properties of the lattice solitons in the incommensurate phase of spin-Peierls systems using exact diagonalization and quantum Monte Carlo simulations. These systems are modeled by an antiferromagnetic Heisenberg chain with nearest- and next-nearest-neighbor interactions coupled to the lattice in the adiabatic approximation. Several relations among features of the solitons and magnetic properties of the system have been determined and compared with analytical predictions. We have studied in particular the relation between the soliton width and the spin-Peierls gap. Although this relation has the form predicted by bosonized field theories, we have found some important quantitative differences which could be relevant to describe experimental studies of spin-Peierls materials.
Abstract We investigate the thermodynamic properties of finite Su–Schrieffer–Heeger chains in thermal equilibrium at fixed temperature and chemical potential. Using the canonical and grand canonical ensembles, we calculate the energy density, particle number density, entropy, and heat capacity as functions of temperature, chemical potential, and hopping asymmetry. Our analysis reveals a double-peak anomaly in the heat capacity for non-dimerized configurations, in which two maxima are separated by a local minimum. We identify this feature as a Schottky-type thermal crossover governed by two distinct energy scales. The anomaly is most pronounced when the chemical potential is comparable to the band scale, and its two maxima separate further as the hopping asymmetry increases and the chain length grows, reflecting the widening gap between the two energy scales and the increasing density of states. We demonstrate that while the topological properties are determined by boundary states, the bulk thermodynamic behavior exhibits a rich crossover structure that can be tuned through the hopping parameter ratio. These findings provide insights into the interplay between topology, finite-size effects, and thermal fluctuations in one-dimensional topological systems, with potential implications for experimental realizations in cold atoms, photonic systems, and topoelectrical circuits.
We study the one-dimensional Holstein model with spin-12\frac{1}{2}21​ electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
We study one-dimensional Su-Schrieffer-Heeger (SSH) models with quantum phonons using a continuous-time quantum Monte Carlo method. Within statistical errors, we obtain identical results for the SSH model with acoustic phonons, and a related model with a coupling to an optical bond phonon mode. Based on this agreement, we first study the Peierls metal-insulator transition of the spinless SSH model, and relate it to the Kosterlitz-Thouless transition of a spinless Luttinger liquid. In the Peierls phase, the spectral functions reveal the single-particle and charge gap, and a central peak related to long-range order. For the spinful SSH model, which has a dimerized ground state for any nonzero coupling, we reveal a symmetry-related degeneracy of spin and charge excitations, and the expected spin and charge gaps as well as a central peak. Finally, we study the SSH-UVUVUV model with electron-phonon and electron-electron interaction. We observe a Mott phase with critical spin and bond correlations at weak electron-phonon coupling, and a Peierls phase with gapped spin excitations at strong coupling. We relate our findings to the extended Hubbard model, and discuss the physical origin of the agreement between optical and acoustic phonons.