Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1903.09983 · Physical review. B./Physical review. B

Determinant quantum Monte Carlo study of exhaustion in the periodic Anderson model

Lufeng Zhang, Tianxing Ma, Natanael C. Costa, Raimundo R. dos Santos, Richard T. Scalettar

Published May 28, 2019• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.99.195147

Related papers

Finite f -electron bandwidth in a heavy-fermion model

Axel Euverte, Simone Chiesa, Richard T. Scalettar +1 more

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.

arXiv:1310.0372•Physical Review B•Dec 20, 2013•5 citations

From Periodic to Dilute Anderson Models

Lucas Hollender

Actinide- and Lanthanide based compounds are often considered as heavy Fermion (HF) systems. The essential ingredient for these systems is a localized d- or f-shell electron per lattice site which hybridizes with a non-interacting conduction band of p- or d-shell electrons. For temperatures below the so called coherence temperature Tc, the localized electrons stop to act like mag- netic scatterers known from the Kondo effect. There the conduction band electrons screen the local magnetic moments coherently. As a main effect the conduction electrons build a Fermi liquid (FL) of quasiparticles with strongly enhanced masses which exceed 10-1000 times the mass of the original electrons. These enhancements can be seen experimentally in an increased heat capacity coefficient and Pauli susceptibility. \nIn this work we employ the periodic Anderson model (PAM) to describe the paramagnetic phase of the heavy Fermion compounds. To solve the compli- cated many body problem the dynamical mean-field theory is adopted with the numerical renormalization group technique as impurity solver. \nWe find that for low conduction band fillings Tc decreases drastically, which is in accordance with the exhaustion effect predicted by Nozières [5]. Additionally we find, that the form of the free conduction band density of states is decisive to obtain a FL or a Mott insulating (MI) phase for strongly depleted conduction band fillings. \nFurthermore we investigate the PAM on a bipartite lattice, the coherence temperatures for each sublattice and especially the case of vanishing hybridiza- tion for one sublattice. In the latter case the system resembles a conduction band with only half the localized moment sites coupled to it. Our results show that it depends strongly on the chosen parameters if there is only one scale for the whole lattice or two distinct scales for each sublattice. Especially decoupling one sublattice leads to two separated scales. \nIn the last part the attention is focused on the two-impurity Anderson model and its solution via the DMFT method. We investigate the Anderson model and compare results to direct NRG calculations. Importantly, the two-impurity DMFT method can be easier extended to multi-impurity systems than the NRG on its own. This might lead to a method to efficiently examine multi- impurity systems.

•Nov 14, 2012•1 citation

Kondo breakdown in multi-orbital Anderson lattices induced by destructive hybridization interference

Fabian Eickhoff, Frithjof B. Anders

In this paper we consider a multi-band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi-liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, T_{K}\propto \exp(-\mathrm{const}\, U/(\Gamma_1+\Gamma_2)) T K ∝ exp ( − c o n s t U / ( Γ 1 + Γ 2 ) ) , we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi-liquid scale T_0\propto \exp(-\mathrm{const}\, U/(\Gamma_1-\Gamma_2)) T 0 ∝ exp ( − c o n s t U / ( Γ 1 − Γ 2 ) ) can emerge due to quantum interference effects in multi-band models, where U U denotes the local Coulomb matrix element of the correlated orbitals and \Gamma_i Γ i the local hybridization strength of band i i . At high symmetry points, heavy Fermi-liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals \propto|\omega|^{1/3} ∝ | ω | 1 / 3 , indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.

arXiv:2401.04540•SciPost Physics•Sep 2, 2024•2 citations

Emergent Properties of the Periodic Anderson Model: A High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality

Andreas Gleis, Seung‐Sup B. Lee, Gabriel Kotliar +1 more

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024

arXiv:2310.12672•Physical Review X•Nov 7, 2024•19 citations

Insulator-to-insulator transition and sign problem in the periodic Anderson model with a staggered potential

Mengfan Wang, Danqing Hu, Yi‐feng Yang

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 $f$-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.

Physical review. B./Physical review. B•Nov 7, 2024•0 citations

Magnetic quantum phase transition in a metallic Kondo heterostructure

Zi Hong Liu, Bernhard Frank, Lukas Janssen +2 more

We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.

arXiv:2211.02071•Physical review. B./Physical review. B•Apr 4, 2023•6 citations
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.
The determinant quantum Monte Carlo (DQMC) method is used to study the effect of nonzero hopping tf{t}_{f}tf​ in the ``localized'' fff band of the periodic Anderson model (PAM) in two dimensions. The low-temperature properties are determined in the plane of interband hybridization VVV and tf{t}_{f}tf​ at fixed Uf{U}_{f}Uf​ and half filling, including the case when the sign of tf{t}_{f}tf​ is opposite to that of the conduction band td{t}_{d}td​. For tf{t}_{f}tf​ and td{t}_{d}td​ of the same sign and when tf/td>(V/4td)2{t}_{f}/{t}_{d}>{(V/4{t}_{d})}^{2}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{U}_{f}=0Uf​=0 persists in the interacting system, manifesting itself as a maximal tendency toward antiferromagnetic correlations at low temperature. In this ``optimal'' tf{t}_{f}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{t}_{f}=0tf​=0) and single-band Hubbard model, where short-range correlations are stronger and develop at higher temperature. The effect that finite tf{t}_{f}tf​ has on Kondo screening is investigated by considering the evolution of the local density of states for selected tf{t}_{f}tf​ as a function of VVV. We use mean-field theory as a tool to discriminate those aspects of the physics that are genuinely many-body in character.
Actinide- and Lanthanide based compounds are often considered as heavy Fermion (HF) systems. The essential ingredient for these systems is a localized d- or f-shell electron per lattice site which hybridizes with a non-interacting conduction band of p- or d-shell electrons. For temperatures below the so called coherence temperature Tc, the localized electrons stop to act like mag- netic scatterers known from the Kondo effect. There the conduction band electrons screen the local magnetic moments coherently. As a main effect the conduction electrons build a Fermi liquid (FL) of quasiparticles with strongly enhanced masses which exceed 10-1000 times the mass of the original electrons. These enhancements can be seen experimentally in an increased heat capacity coefficient and Pauli susceptibility. \nIn this work we employ the periodic Anderson model (PAM) to describe the paramagnetic phase of the heavy Fermion compounds. To solve the compli- cated many body problem the dynamical mean-field theory is adopted with the numerical renormalization group technique as impurity solver. \nWe find that for low conduction band fillings Tc decreases drastically, which is in accordance with the exhaustion effect predicted by Nozières [5]. Additionally we find, that the form of the free conduction band density of states is decisive to obtain a FL or a Mott insulating (MI) phase for strongly depleted conduction band fillings. \nFurthermore we investigate the PAM on a bipartite lattice, the coherence temperatures for each sublattice and especially the case of vanishing hybridiza- tion for one sublattice. In the latter case the system resembles a conduction band with only half the localized moment sites coupled to it. Our results show that it depends strongly on the chosen parameters if there is only one scale for the whole lattice or two distinct scales for each sublattice. Especially decoupling one sublattice leads to two separated scales. \nIn the last part the attention is focused on the two-impurity Anderson model and its solution via the DMFT method. We investigate the Anderson model and compare results to direct NRG calculations. Importantly, the two-impurity DMFT method can be easier extended to multi-impurity systems than the NRG on its own. This might lead to a method to efficiently examine multi- impurity systems.
In this paper we consider a multi-band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi-liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, T_{K}\propto \exp(-\mathrm{const}\, U/(\Gamma_1+\Gamma_2)) T K ∝ exp ( − c o n s t U / ( Γ 1 + Γ 2 ) ) , we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi-liquid scale T_0\propto \exp(-\mathrm{const}\, U/(\Gamma_1-\Gamma_2)) T 0 ∝ exp ( − c o n s t U / ( Γ 1 − Γ 2 ) ) can emerge due to quantum interference effects in multi-band models, where U U denotes the local Coulomb matrix element of the correlated orbitals and \Gamma_i Γ i the local hybridization strength of band i i . At high symmetry points, heavy Fermi-liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals \propto|\omega|^{1/3} ∝ | ω | 1 / 3 , indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.
We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024
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.
We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.