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Feynman Path‐Integral Quantum Monte‐Carlo Simulations of One‐Dimensional Chains in the Presence of Attractive Intersite Interactions

Michael C. Böhm, J. Schulte, Luis Utrera

Published Apr 1, 1993• 2 citations
Publisher

Abstract

Abstract Feynman path‐integral quantum Monte‐Carlo (QMC) simulations are employed to investigate the ground‐state properties of the one‐dimensional Hubbard chain in the presence of attractive intersite interactions V. With increasing magnitude of the V elements the formation of domain structures causing a violation of the translational symmetry within the ID chain is observed. Domain structures differ from on‐site charge density wave (CDW) configurations in so far as their charge distribution shows random behaviour. The on‐site CDW is highly ordered. It is suggested that condensation transitions are position‐space concomitants of superconducting configurations of the ID chain. The formation of symmetry‐breaking domains is attenuated in ID chains with an average electron density 〈n〉 of 1.0. The dynamics of the electronic and spin degrees of freedom is studied by the fluctuations of the electronic charges 〈(Δn2)〉 and the local magnetic moments 〈(Δs2)〉.

DOI
10.1002/pssb.2221760214

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Abstract Feynman path‐integral quantum Monte‐Carlo (QMC) simulations are employed to investigate the ground‐state properties of the one‐dimensional Hubbard chain in the presence of attractive intersite interactions V. With increasing magnitude of the V elements the formation of domain structures causing a violation of the translational symmetry within the ID chain is observed. Domain structures differ from on‐site charge density wave (CDW) configurations in so far as their charge distribution shows random behaviour. The on‐site CDW is highly ordered. It is suggested that condensation transitions are position‐space concomitants of superconducting configurations of the ID chain. The formation of symmetry‐breaking domains is attenuated in ID chains with an average electron density 〈n〉 of 1.0. The dynamics of the electronic and spin degrees of freedom is studied by the fluctuations of the electronic charges 〈(Δn2)〉 and the local magnetic moments 〈(Δs2)〉.
Feynman path-integral quantum Monte Carlo (QMC) simulations and an analytic many-body approach are used to study the ground state properties of one-dimensional (1D) chains in the theoretical framework of model Hamiltonians of the Hubbard type. The QMC algorithm is employed to derive position-space quantities, while band structure properties are evaluated by combining QMC data with expressions derived in momentum (k) space. Bridging link between both representations is the quasi-chemical approximation (QCA). Electronic charge fluctuations <(Δn 2 i )> and the fluctuations of the magnetic local moments <(Δs 2 i )> are studied as a function of the on-site density <n i > and correlation strength, which is given by the ratio between two-electron interaction and kinetic hopping. Caused by the non-analytic behaviour of the chemical potential μ = ∂E/∂<n i > (with E denoting the electronic energy), strict 1D systems with an on-site density <n i > of 1·0 do not exhibit the properties of a conductor for any non-zero interaction beyond the mean-field approximation. The QMC simulations lead to straightforward access to the probabilities P i (n) of finding n = 0, 1, 2 electrons at the ith lattice site. The P i (n) elements allow to calculate the enhancement factors on the electron spin susceptibility χ, effective electronic mass m* and Knight shift κ. m* is enhanced by a bandwidth renormalization factor D -1 0, κ by an element ηK mapping the additional localization of the correlated electrons in the presence of an external magnetic field B and χ by the product D -1 0 ηK. Available experimental data are discussed in the light of the present theoretical findings.
Strongly correlated materials exhibit some of the most complex and technologically useful phenomena in condensed matter. We use the world line and determinant quantum Monte Carlo techniques to explore the phases of the Hubbard Hamiltonian, a model describing strong interactions, in a number of different contexts. We first consider the spin, charge, and bond order correlations of the one-dimensional extended fermion Hubbard model in the presence of a coupling to the lattice. A static alternating lattice distortion leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic, we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases. Second, we examine mixtures of bosons and fermions in one-dimensional optical lattices. We evaluate the density profiles and bosonic visibility [special characters omitted] resolving the discrepancy between theory and experiment by identifying parameter regimes where [special characters omitted] is reduced and increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that [special characters omitted] exhibits kinks which are tied to the domain evolution present in the pure bosonic case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments. Third, we report large scale calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the momentum distribution, allowing a more quantitative comparison with time-of-flight optical lattice experiments.
Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.
We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above Tc{T}_{c}Tc​ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.
The half-filled attractive Hubbard model exhibits a simultaneous charge-density wave and superconducting order in its ground state. In this paper we use approximation-free quantum Monte Carlo techniques to explore the effect of disorder in the site energies on this degeneracy. We find that superconducting order survives randomness out to a critical amount of disorder, but charge ordering is immediately destroyed. This settles the issue as to whether disordered site energies, which do not break time-reversal invariance, can destroy pairing correlations. We also locate the precise ratio of disorder to bandwidth required for the disorder-driven transition from the superconducting state. We explore the validity of a strong-coupling picture which maps the system onto a Heisenberg model in a random magnetic field.