Monte Carlo study of the symmetric Anderson-impurity model

Fye, R. M.; Hirsch, J. E.

doi:10.1103/physrevb.38.433

Cited by 89 publications

(69 citation statements)

References 16 publications

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“…We did not observe any major difference in the characteristics of the DQMC algorithm in simulating the dynamic Hubbard model: Autocorrelation times remain short, as is typically the case with DQMC, and there was no major change in the numerical stability 3,23,24,25 . The key issue in DQMC is the 'sign problem' which we will discuss in the following sections.…”

Section: Methodsmentioning

confidence: 86%

Sign change of the extendeds-wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study

et al. 2008

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The 'dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant Quantum Monte Carlo method. Our key result is that the extended s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.

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Section: Methodsmentioning

confidence: 86%

Sign change of the extendeds-wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study

et al. 2008

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“…In the determinantal Monte Carlo (the Hirsch and Fye algorithm) the impurity susceptibility is very difficult to calculate due to statistical noises in the simulation [21]. The problem is that one has to calculate the total susceptibility for the Anderson Hamiltonian and then subtract the susceptibility for the free case from it.…”

Section: Observablesmentioning

confidence: 99%

“…Finally, some observables are difficult to evaluate. One famous example is the impurity susceptibility which is known to contain large fluctuations [21].…”

Section: Introductionmentioning

confidence: 99%

Multilevel algorithm for quantum-impurity models

2005

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A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low temperatures, the new algorithm has many advantages over conventional algorithms. For example, the model can be easily simulated in the Kondo limit without time discretization errors. Further, many observables including the impurity susceptibility and a variety of fermionic observables can be calculated efficiently. Finally the new approach allows us to explore a general technique, called the multi-level algorithm, to solve the sign problem. We find that the multi-level algorithm is able to generate an exponentially large number of configurations with an effort that grows as a polynomial in inverse temperature such that configurations with a positive sign dominate over those with negative signs. Our algorithm can be easily generalized to other multi-impurity problems.

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“…Numerical efforts, which are necessary for the existing numerical methods (e.g., numerical renormalization group (NRG) [39], quantum Monte Carlo [40,41], continuous-time quantum Monte Carlo [42], exact diagonalization [43][44][45], nano-DMFT [46][47][48][49][50][51], and nano-DΓA [48,52]) grow fast with increasing system size or asymmetry, such that the comprehensive analysis of complex quantum dot systems (especially the conductance) is rather difficult for purely numerical methods. Therefore, developing and using semi-analytical techniques is important for description of such systems.…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings

Проценко

Катанин

2017

Phys. Rev. B

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We explore the effects of asymmetry of hopping parameters between double parallel quantum dots and the leads on the conductance and a possibility of local magnetic moment formation in this system using functional renormalization group approach with the counterterm. We demonstrate a possibility of a quantum phase transition to a local moment regime (so called singular Fermi liquid (SFL) state) for various types of hopping asymmetries and discuss respective gate voltage dependences of the conductance. It is shown, that depending on the type of the asymmetry, the system can demonstrate either a first order quantum phase transition to SFL state, accompanied by a discontinuous change of the conductance, similarly to the symmetric case, or the second order quantum phase transition, in which the conductance is continuous and exhibits Fano-type asymmetric resonance near the transition point. A semi-analytical explanation of these different types of conductance behavior is presented.

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Monte Carlo study of the symmetric Anderson-impurity model

Cited by 89 publications

References 16 publications

Sign change of the extendeds-wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study

Sign change of the extendeds-wave pairing vertex in the dynamic Hubbard model: A quantum Monte Carlo study

Multilevel algorithm for quantum-impurity models

Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings

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