48 research outputs found
Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
The two-dimensional Holstein-Hubbard model is studied by means of
continuous-time quantum Monte Carlo simulations. Using
renormalization-group-invariant correlation ratios and finite-size
extrapolation, the critical temperature of the charge-density-wave transition
is determined as a function of coupling strength, phonon frequency, and Hubbard
repulsion. The phase transition is demonstrated to be in the universality class
of the two-dimensional Ising model and detectable via the fidelity
susceptibility. The structure of the ground-state phase diagram and the
possibility of a bipolaronic metal with a single-particle gap above are
explored.Comment: 8 pages, 9 figures; expanded version including Holstein-Hubbard
result
Correlated atomic wires on substrates. II. Application to Hubbard wires
In the first part of our theoretical study of correlated atomic wires on
substrates, we introduced lattice models for a one-dimensional quantum wire on
a three-dimensional substrate and their approximation by quasi-one-dimensional
effective ladder models [arXiv:1704.07350]. In this second part, we apply this
approach to the case of a correlated wire with a Hubbard-type electron-electron
repulsion deposited on an insulating substrate. The ground-state and spectral
properties are investigated numerically using the density-matrix
renormalization group method and quantum Monte Carlo simulations. As a function
of the model parameters, we observe various phases with quasi-one-dimensional
low-energy excitations localized in the wire, namely paramagnetic Mott
insulators, Luttinger liquids, and spin- Heisenberg chains. The validity
of the effective ladder models is assessed by studying the convergence with the
number of legs and comparing to the full three-dimensional model. We find that
narrow ladder models accurately reproduce the quasi-one-dimensional excitations
of the full three-dimensional model but predict only qualitatively whether
excitations are localized around the wire or delocalized in the
three-dimensional substrate
Ground-state and spectral properties of an asymmetric Hubbard ladder
We investigate a ladder system with two inequivalent legs, namely a Hubbard
chain and a one-dimensional electron gas. Analytical approximations, the
density matrix renormalization group method, and continuous-time quantum Monte
Carlo simulations are used to determine ground-state properties, gaps, and
spectral functions of this system at half-filling. Evidence for the existence
of four different phases as a function of the Hubbard interaction and the rung
hopping is presented. First, a Luttinger liquid exists at very weak interchain
hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an
effective rung exchange coupling is found at moderate interchain hopping or
strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator
with incommensurate excitations and pairing of doped charges is observed at
intermediate values of the rung hopping and the interaction. Fourth, the usual
correlated band insulator is recovered for large rung hopping. We show that the
wavenumbers of the lowest single-particle excitations are different in each
insulating phase. In particular, the three gapped phases exhibit markedly
different spectral functions. We discuss the relevance of asymmetric two-leg
ladder systems as models for atomic wires deposited on a substrate.Comment: published versio
Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
We extend the continuous-time interaction-expansion quantum Monte Carlo
method with respect to measuring observables for fermion-boson lattice models.
Using generating functionals, we express expectation values involving boson
operators, which are not directly accessible because simulations are done in
terms of a purely fermionic action, as integrals over fermionic correlation
functions. We also demonstrate that certain observables can be inferred
directly from the vertex distribution, and present efficient estimators for the
total energy and the phonon propagator of the Holstein model. Furthermore, we
generalize the covariance estimator of the fidelity susceptibility, an unbiased
diagnostic for phase transitions, to the case of retarded interactions. The new
estimators are applied to half-filled spinless and spinful Holstein models in
one dimension. The observed renormalization of the phonon mode across the
Peierls transition in the spinless model suggests a soft-mode transition in the
adiabatic regime. The critical point is associated with a minimum in the phonon
kinetic energy and a maximum in the fidelity susceptibility.Comment: 12 pages, 4 figures, 1 table; final versio