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arXiv:cond-mat/0412217 · Journal of the Physical Society of Japan

NRG Approach to the Transport through a Finite Hubbard Chain Connected to Reservoirs

Akira Oguri, Alex C. Hewson

Published Mar 1, 2005• 30 citations
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Abstract

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.

DOI
10.1143/jpsj.74.988

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We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.
We study the effects of electron correlation on transport through a small interacting system connected to reservoirs using an effective Hamiltonian which describes the free quasiparticles of a Fermi liquid. The effective Hamiltonian is defined microscopically with the value of the self-energy at $\ensuremath{\omega}=0.$ Specifically, we apply the method to a Hubbard chain of finite size N (=1,2,3,…),(=1,2,3,\dots{}),(=1,2,3,…), and calculate the self-energy within the second order in U in the electron-hole-symmetric case. When couplings between the chain and the reservoirs on the left and right are small, the conductance for even N decreases with increasing N, showing a tendency toward a Mott-Hubbard insulator. This is caused by the off-diagonal element of the self-energy, and this behavior is qualitatively different from that in the special case examined in previous work. We also study the effects of the asymmetry in the two couplings. While a perfect transmission due to the Kondo resonance occurs for any odd N in the symmetric coupling, the conductance for odd N decreases with increasing N in the case of asymmetric coupling.
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We describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case.
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