The determinant quantum Monte Carlo (DQMC) method is used to study the effect of nonzero hopping
tf in the ``localized''
f band of the periodic Anderson model (PAM) in two dimensions. The low-temperature properties are determined in the plane of interband hybridization
V and
tf at fixed
Uf and half filling, including the case when the sign of
tf is opposite to that of the conduction band
td. For
tf and
td of the same sign and when
tf/td>(V/4td)2, the noninteracting system is metallic. We show that a remnant of the band insulator to metal line at
Uf=0 persists in the interacting system, manifesting itself as a maximal tendency toward antiferromagnetic correlations at low temperature. In this ``optimal''
tf region, short-range (e.g., near-neighbor) and long-range spin correlations develop at similar temperatures and have comparable magnitude. Both observations are in stark contrast to the situation in the widely studied PAM (
tf=0) and single-band Hubbard model, where short-range correlations are stronger and develop at higher temperature. The effect that finite
tf has on Kondo screening is investigated by considering the evolution of the local density of states for selected
tf as a function of
V. We use mean-field theory as a tool to discriminate those aspects of the physics that are genuinely many-body in character.
The Kondo and periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling
J or hybridization
V between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small
J or
V, limit, the moments survive and the conduction electrons mediate an effective interaction which can trigger long-range, often antiferromagnetic order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting ``exhaustion'' problem and how the ``coherence temperature'' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low-temperature quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical
V for the singlet-antiferromagnetic transition.
We report preliminary results of an investigation of the thermodynamic properties of the extended Hubbard model in one- dimension, calculated with the world-line Monte Carlo method described by Hirsch et al. With strictly continuous world-lines, we are able to measure the expectation of operators that conserve fermion number locally, such as the energy and (spatial) occupation number. By permitting the world-lines to be broken'' stochastically, we may also measure the expectation of operators that conserve fermion number only globally, such as the single-particle Green's function. For a 32 site lattice we present preliminary calculations of the average electron occupancy as a function of wavenumber when U = 4, V = 0 and {beta} = 16. For a half-filled band we find no indications of a Fermi surface. Slightly away from half-filling, we find Fermi-surface-like behavior similar to that found in other numerical investigations. 8 refs., 3 figs.
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The
f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the
f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons,
Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare
f level, where heavy-fermion behavior can be observed. For large-enough
Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while
Ud enhances the quasiparticle mass when the filling is close to half filling.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via
Z2 antiferromagnetic quantum critical fluctuations by means of a sign-problem-free quantum Monte Carlo approach. We show that the phase diagram of this model indeed contains a
d-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above
Tc, exhibiting hallmark strange-metal transport phenomenology. Interestingly, we find that this version of the model describes a non-Fermi-liquid metallic regime that displays an approximately
T-linear resistivity above
Tc for a strong fermion-boson interaction. Using the Nernst-Einstein relation, our QMC results also show that this strange metal phase exhibits a crossover from being characterized by a charge compressibility given approximately by ${\ensuremath{\chi}}_{c}\ensuremath{\sim}1/T$ at high temperatures to being described by a charge diffusivity consistent with the scaling ${D}_{c}\ensuremath{\sim}1/T$ at low temperatures. Therefore, our paper adds support to the view that the
Z2 antiferromagnetic spin-fermion model at strong coupling can be considered a minimal model that describes both unconventional superconductivity and strange metallicity, which are fundamentally interconnected in many important strongly correlated quantum materials.
Quantum Monte Carlo[MC] calculation of one-dimensional periodic Anderson model without orbital degeneracy is performed by use of the path-integral formulation. Local f moment coincides well with the recent MC calculation for single impurity by Hirsch and Fye above the temperature at which antiferromagnetic correlation starts to grow, and decreases faster than those for single impurity and coupled two impurities below that temperature. Overall features, including susceptibilities, resemble one-dimensional Hubbard model with half-filled band.