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arXiv:1310.0372 · Physical Review B

Finite f -electron bandwidth in a heavy-fermion model

Axel Euverte, Simone Chiesa, Richard T. Scalettar, G. G. Batrouni

Published Dec 20, 2013• 5 citations
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Abstract

The determinant quantum Monte Carlo (DQMC) method is used to study the effect of nonzero hopping ${t}_{f}$ 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 ${t}_{f}$ at fixed ${U}_{f}$ and half filling, including the case when the sign of ${t}_{f}$ is opposite to that of the conduction band ${t}_{d}$. For ${t}_{f}$ and ${t}_{d}$ of the same sign and when ${t}_{f}/{t}_{d}>{(V/4{t}_{d})}^{2}$, the noninteracting system is metallic. We show that a remnant of the band insulator to metal line at ${U}_{f}=0$ persists in the interacting system, manifesting itself as a maximal tendency toward antiferromagnetic correlations at low temperature. In this ``optimal'' ${t}_{f}$ 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 (${t}_{f}=0$) and single-band Hubbard model, where short-range correlations are stronger and develop at higher temperature. The effect that finite ${t}_{f}$ has on Kondo screening is investigated by considering the evolution of the local density of states for selected ${t}_{f}$ 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.

DOI
10.1103/physrevb.88.235123

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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 JJJ or hybridization VVV between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small JJJ or VVV, 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 VVV for the singlet-antiferromagnetic transition.
We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two-band fermion Hubbard model using determinant quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFMO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that LRAFMO plays a key role in the transitions.
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Motivated by the recent proposal that the Monte Carlo sign problem might be used as an indicator of quantum phase transitions, we simulate the periodic Anderson model at half-filling with a staggered ionic potential using the determinant quantum Monte Carlo (DQMC) approach. We observe a phase transition from a band insulator to a Kondo insulator as the hybridization increases. At finite temperature, an intermediate metallic region emerges between two insulating phases, which is characterized by a pseudogap in the spectral functions near the boundary of the intermediate region and a quasiparticle peak in the middle. The latter coincides with a crossing point of the fff-electron occupation on different sublattices as well as the maximum antiferromagnetic (AFM) correlations. The metallic region extrapolates to a single quantum critical point at zero temperature, which may result in exotic quasiparticle excitations associated with the emergent metallic state. The Monte Carlo sign problem is found to be most pronounced in the quantum critical region, implying a close connection between the two phenomena. Our results are qualitatively supported by the Hartree-Fock (HF) mean-field calculations. Our work reveals interesting physics in inhomogeneous Kondo lattice systems that may be worthwhile of more investigations in the future.
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