Natural orbitals renormalization group approach to a Kondo singlet

Zheng, Ru; He, Rong-Qiang; Lu, Zhong-Yi

doi:10.1007/s11433-019-1520-3

Cited by 10 publications

(11 citation statements)

References 110 publications

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“…After all, the Kondo screening cloud is typically much larger than the Fermi wavelength and thus encompasses many conduction electrons. However, recent studies have come to a different and seemingly paradoxical conclusion [17,18]. These works considered the one-body density matrix (also called the correlation matrix) [19][20][21] of the Kondo problem.…”

Section: Introductionmentioning

confidence: 99%

“…The remaining orbitals are called active and host correlated particles. One study [18] found that there is a single active orbital that is "solely responsible for screening the impurity spin in both the weak and strong Kondo coupling regime," and that the resulting singlet is disentangled from the rest of the system. The authors of another study [17] similarly report that they have identified "a dominant single particle wave function that is entangled to the impurity forming a singlet that is, to a great extent, practically disentangled from the rest of the conduction electrons."…”

Section: Introductionmentioning

confidence: 99%

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Few-body nature of Kondo correlated ground states

2021

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The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wave function. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine manybody correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite-size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Few-body nature of Kondo correlated ground states

2021

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“…48 for details), a newly developed numerical many-body approach without perturbation, to study the magnetic correlation between the two Kondo impurities. It has been demonstrated that the NORG method works efficiently on quantum impurity models in the whole coupling regime 29,48,[58][59][60] . Moreover, the NORG method preserves the whole geometric information of a lattice and its effectiveness is independent of any topological structure of a lattice.…”

Section: B Numerical Methodsmentioning

confidence: 99%

Magnetic correlation between two local spins in a quantum spin Hall insulator

Zheng,

He,

2022

Preprint

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Two spins located at the edge of a quantum spin Hall insulator (QSHI) may interact with each other via indirect spin-exchange interaction mediated by the helical edge states, namely the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which can be measured by the magnetic correlation between the two spins. By means of the newly developed natural orbitals renormalization group (NORG) method, we investigated the magnetic correlation between two Kondo impurities interacting with the helical edge states, based on the Kane-Mele (KM) model defined in a finite zigzag graphene nanoribbon (ZGNR) with spin-orbital coupling (SOC). We find that the SOC effect breaks the symmetry in spatial distribution of the magnetic correlation, leading to anisotropy in the RKKY interaction. Specifically, the total correlation is always ferromagnetic (FM) when the two impurities are located at the same sublattice, while it is always antiferromagnetic (AFM) when at the different sublattices. Meanwhile, the behavior of the in-plane correlation is consistent with that of the total correlation. However, the out-of-plane correlation can be tuned from FM to AFM by manipulating either the Kondo coupling or the interimpurity distance. Furthermore, the magnetic correlation is tunable by the SOC, especially that the out-of-plane correlation can be adjusted from FM to AFM by increasing the strength of SOC. Dynamic properties of the system, represented by the spin-staggered excitation spectrum and the spin-staggered susceptibility at the two impurity sites, are finally explored. It is shown that the spin-staggered susceptibility is larger when the two impurities are located at the different sublattices than at the same sublattice, which is consistent with the behavior of the out-of-plane correlation. On the other hand, our study further demonstrates that the NORG is an effective numerical method for studying the quantum impurity systems.

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“…Although a quantum impurity system is also electronically correlated, its correlation is very different from a regular strongly correlated system in that the impurities can only entangle with a finite number of degrees of freedom in the bath, which we call sparse correlation [42]. Consequently, the ground state is, in some sense, simple [43][44][45] and can be approximately but accurately represented in a very small subspace of the complete Hilbert space. The NRG [16,17] finds this subspace by selecting many-body basis according to energy (the eigenvalues of the Hamiltonian), the DMRG [18][19][20][21][22][23][24][25] does this by selecting many-body basis according to entanglement (the eigenvalues of the reduced density matrix), while the recently proposed natural orbitals renormalization group (NORG) [42] does this by selecting many-body basis according to natural orbital occupancies (the eigenvalues of the single-particle density matrix).…”

Section: Introductionmentioning

confidence: 99%

Solving multiorbital dynamical mean-field theory using natural orbitals renormalization group

Wang¹,

Chen²,

Tian³

et al. 2022

Preprint

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The natural orbitals renormalization group (NORG) has previously been proposed as an efficient numerical method for solving zero-temperature properties of multisite and multiorbital quantum impurity systems. Here, we implement the NORG as an impurity solver for dynamical mean-field theory (DMFT). In comparison with the exact diagonalization method, the NORG method can treat much more bath sites in an impurity model to which the DMFT maps a lattice model and can find accurate zero-temperature Matsubara and low-frequency retarded Green's functions. We demonstrate the effectiveness of this method on a two-orbital Hubbard model on the Bethe lattice and find successfully the orbital selective Mott transition with a Kondo resonance peak in the wide band and two holon-doublon bound state excitation peaks in the narrow band.

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Natural orbitals renormalization group approach to a Kondo singlet

Cited by 10 publications

References 110 publications

Few-body nature of Kondo correlated ground states

Few-body nature of Kondo correlated ground states

Magnetic correlation between two local spins in a quantum spin Hall insulator

Solving multiorbital dynamical mean-field theory using natural orbitals renormalization group

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