The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums
of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.
We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon f
requency $omega_0 = 0.1 t$. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant $2k_f$ charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for within a self-consistent Born approximation. In the low temperature Luttinger liquid phase we observe features which compare favorably with a bosonization approach retaining only forward scattering. In the Luther-Emery phase, the spectral function at low temperatures shows a quasiparticle gap which matches half the spin gap whereas at temperatures above which this quasiparticle gap closes, characteristic features of the Luttinger liquid model are apparent. Our results are based on lattice simulations on chains up to L=20 for two-particle properties and on CDMFT calculations with clusters up to 12 sites for the single-particle spectral function.
We study the temperature dependence of the single particle spectral function as well as of the dynamical spin and charge structure factors for the one-dimensional Hubbard model using the finite temperature auxiliary field quantum Monte Carlo algorith
m. The parameters of our simulations are chosen so to at best describe the low temperature photoemission spectra of the organic conductor TTF-TCNQ. Defining a magnetic energy scale, T_J, which marks the onset of short ranged 2k_f magnetic fluctuations, we conclude that for temperatures T < T_J the ground state features of the single particle spectral function are apparent in the finite temperature data. Above T_J spectral weight transfer over a scale set by the hopping t is observed. In contrast, photoemission data points to a lower energy scale below which spectral weight transfer occurs. Discrepancies between Hubbard model calculations and experiments are discussed.
