The periodic Anderson model: Symmetry-based results and some exact solutions

Noce, Canio

doi:10.1016/j.physrep.2006.05.003

Cited by 24 publications

(4 citation statements)

References 115 publications

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“…This kind of procedure has been previously applied by Auerbach to exclude magnetic order in the Heisenberg model in one dimension [37] and by Su et al to the low-dimensional Hubbard model [30]. On a more general note, it has been rigorously shown that if the energy spectrum has a gap then the model under investigation does not exhibit long-range-order at T = 0, and this energy gap plays the role of temperature in the conventional Bogoliubov inequality [38,39]. We plan to investigate this issue in the near future, focusing on the model Hamiltonian equation (3) analyzed here.…”

Section: Remarks and Conclusionmentioning

confidence: 99%

Nematic order in a degenerate Hubbard model with spin–orbit coupling

Guarnaccia¹,

Noce²

2013

J. Phys.: Condens. Matter

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Section: Remarks and Conclusionmentioning

confidence: 99%

Nematic order in a degenerate Hubbard model with spin–orbit coupling

Guarnaccia¹,

Noce²

2013

J. Phys.: Condens. Matter

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“…We are thus naturally led to the analysis of the two-orbital Hubbard model in this limit, applied to the case of an infinite lattice. Though rather artificial as far as its possible applications to real systems are concerned, this limit has its main virtue in its tractability, so that it has often been studied in the past in connection with several correlated electron models, such as the Hubbard model [37], the t-J model [38], the Kondo lattice model [39] and the Anderson lattice model [40].…”

Section: The Infinite Range Hopping Limitmentioning

confidence: 99%

High-spin magnetic states in the two-orbital Hubbard model on a tetrahedron

Romano¹,

Noce²,

Amendola³

2008

J. Phys.: Condens. Matter

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We present a study of the two-orbital degenerate Hubbard model in which the exact numerical solution on a regular tetrahedron is obtained via suitable implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. In particular, we show that a large variety of high-spin magnetic ground states can develop away from half filling, depending on the values of the electron density and the parameters of the model. As the tetrahedron is the simplest finite-size cluster where hopping processes connect all pairs of sites with constant probability, the study is extended by providing the exact analytical solution of the model on an infinite lattice in the unconstrained hopping limit.

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“…Here, the efficiency of variational quantum algorithms in the determination of the ground-state energy is evaluated for a well-known model of interacting electrons, i.e. the Anderson model [11], which is of particular interest for several reasons: first, its theoretical properties are far from being fully understood [12]; second, it is believed to be relevant to physical phenomena ranging from the magnetism to superconductivity and orbital physics [13]; third, its specific structure and relatively simple form suggest that it may be easier to implement on a near-term quantum computer than, for example, model systems occurring in quantum chemistry [14].…”

Section: Introductionmentioning

confidence: 99%

Ansatz optimization of the variational quantum eigensolver tested on the atomic Anderson model

De Riso,

Cipriani,

Villani

et al. 2024

New J. Phys.

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We present a detailed analysis and optimization of the variational quantum algorithms required to find the ground state of a correlated electron model, using several types of variational ansatz. Specifically, we apply our approach to the atomic limit of the Anderson model, which is widely studied in condensed matter physics since it can simulate fundamental physical phenomena, ranging from magnetism to superconductivity. The method is developed by presenting efficient state preparation circuits that exhibit total spin, spin projection, particle number and time-reversal symmetries. These states contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace allowing to avoid irrelevant sectors of Hilbert space. Then, we show how to construct quantum circuits, providing explicit decomposition and gate count in terms of standard gate sets. We test these quantum algorithms looking at ideal quantum computer simulations as well as implementing quantum noisy simulations. We finally perform an accurate comparative analysis among the approaches implemented, highlighting their merits and shortcomings.

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The periodic Anderson model: Symmetry-based results and some exact solutions

Cited by 24 publications

References 115 publications

Nematic order in a degenerate Hubbard model with spin–orbit coupling

Nematic order in a degenerate Hubbard model with spin–orbit coupling

High-spin magnetic states in the two-orbital Hubbard model on a tetrahedron

Ansatz optimization of the variational quantum eigensolver tested on the atomic Anderson model

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