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International Journal of Modern Physics B

QUANTUM MONTE CARLO SIMULATION STUDY OF ONE-DIMENSIONAL PERIODIC ANDERSON MODEL

Meenakshi Sharma, KAMLESH KUMARI, Ishwar S Singh

Published Dec 30, 1999• 0 citations
Publisher

Abstract

Many rare earth and actinide intermetallics, known as Heavy Fermion Systems, have recently been successfully described by the Periodic Anderson Model. We investigate, in this work, various electronic and magnetic properties of the one-dimensional Periodic Anderson model using path integral formulation along with the quantum Monte Carlo simulation technique. We have studied the singlet and triplet pairing correlation functions, nearest neighbor charge-density correlations, spin density correlations, local squared magnetic moment and probability of double occupancy of f-electrons, as a function of intra-atomic Coulomb interaction for various values of hybridization parameter and the temperatures.

DOI
10.1142/s0217979299004094

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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.
We have studied the one-dimensional periodic, symmetric Anderson model at half filling in the presence of disorder using finite-temperature quantum Monte Carlo techniques. We have examined for the first time the disorder both in hybridization between the local f-orbitals and the conduction electrons and in the local f-site energy, using a uniform distribution of width . The f-orbital local magnetic moment, the uniform magnetic susceptibility, the charge compressibility, and the nearest-neighbour magnetic correlation function have been calculated as a function of the disorder distribution width . We find that the disorder in hybridization has a dramatic effect on the low-temperature magnetic properties exhibiting a non-Fermi-liquid behaviour, and that for the range of temperature studied the magnetic susceptibility can be scaled by a power law with an exponent that is in agreement with recent experiments. On the other hand, disorder in the local f-orbital energy level does not show a nonFermi liquid behaviour.
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.