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Register a new userLangevin Simulations of a Long Range Electron Phonon Model
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We present a Quantum Monte Carlo (QMC) study, based on the Langevin equation, of a Hamiltonian describing electrons coupled to phonon degrees of freedom. The bosonic part of the action helps control the variation of the field in imaginary time. As a consequence, the iterative conjugate gradient solution of the fermionic action, which depends on the boson coordinates, converges more rapidly than in the case of electron-electron interactions, such as the Hubbard Hamiltonian. Fourier Acceleration is shown to be a crucial ingredient in reducing the equilibration and autocorrelation times. After describing and benchmarking the method, we present results for the phase diagram focusing on the range of the electron-phonon interaction. We delineate the regions of charge density wave formation from those in which the fermion density is inhomogeneous, caused by phase separation. We show that the Langevin approach is more efficient than the Determinant QMC method for lattice sizes $N gtrsim 8 times 8$ and that it therefore opens a potential path to problems including, for example, charge order in the 3D Holstein model.
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The electron-phonon interaction is of central importance for the electrical and thermal properties of solids, and its influence on superconductivity, colossal magnetoresistance, and other many-body phenomena in correlated-electron materials is currently the subject of intense research. However, the non-local nature of the interactions between valence electrons and lattice ions, often compounded by a plethora of vibrational modes, present formidable challenges for attempts to experimentally control and theoretically describe the physical properties of complex materials. Here we report a Raman scattering study of the lattice dynamics in superlattices of the high-temperature superconductor $bf YBa_2 Cu_3 O_7$ and the colossal-magnetoresistance compound $bf La_{2/3}Ca_{1/3}MnO_{3}$ that suggests a new approach to this problem. We find that a rotational mode of the MnO$_6$ octahedra in $bf La_{2/3}Ca_{1/3}MnO_{3}$ experiences pronounced superconductivity-induced lineshape anomalies, which scale linearly with the thickness of the $bf YBa_2 Cu_3 O_7$ layers over a remarkably long range of several tens of nanometers. The transfer of the electron-phonon coupling between superlattice layers can be understood as a consequence of long-range Coulomb forces in conjunction with an orbital reconstruction at the interface. The superlattice geometry thus provides new opportunities for controlled modification of the electron-phonon interaction in complex materials.
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $xi$, interpolating between the Holstein and Frohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $xi$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U e 0$ case, even for small values of the coupling range.
Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.
Establishing a minimal microscopic model for cuprates is a key step towards the elucidation of a high-$T_c$ mechanism. By a quantitative comparison with a recent emph{in situ} angle-resolved photoemission spectroscopy measurement in doped 1D cuprate chains, our simulation identifies a crucial contribution from long-range electron-phonon coupling beyond standard Hubbard models. Using reasonable ranges of coupling strengths and phonon energies, we obtain a strong attractive interaction between neighboring electrons, whose strength is comparable to experimental observations. Non-local couplings play a significant role in the mediation of neighboring interactions. Considering the structural and chemical similarity between 1D and 2D cuprate materials, this minimal model with long-range electron-phonon coupling will provide important new insights on cuprate high-$T_C$ superconductivity and related quantum phases.
We use Langevin sampling methods within the auxiliary-field quantum Monte Carlo algorithm to investigate the phases of the Su-Schrieffer-Heeger model on the square lattice at the O(4) symmetric point. Based on an explicit determination of the density of zeros of the fermion determinant, we argue that this method is efficient in the adiabatic limit. By analyzing dynamical and static quantities of the model, we demonstrate that a $(pi,pi)$ valence bond solid gives way to an antiferromagnetic phase with increasing phonon frequency.
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