Finite-size corrections for the low lying states of a half-filled Hubbard chain

Woynarovich, F.; Eckle, Hans-Peter

doi:10.1088/0305-4470/20/7/005

Cited by 75 publications

(57 citation statements)

References 12 publications

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“…Finite-size effects at zero temperature have been studied by many authors in connection with the application of conformal field theory [11][12][13][14] . We generalize their method to the case of finite temperatures.…”

Section: Finite-size Corrections To the Thermodynamic Bethe Ansatmentioning

confidence: 99%

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

Fujimoto

Kawakami

1998

J. Phys. A: Math. Gen.

126

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The Drude weight for the one-dimensional Hubbard model is investigated at finite temperatures by using the Bethe ansatz solution. Evaluating finite-size corrections to the thermodynamic Bethe ansatz equations, we obtain the formula for the Drude weight as the response of the system to an external gauge potential. We perform low-temperature expansions of the Drude weight in the case of half-filling as well as away from half-filling, which clearly distinguish the Mott-insulating state from the metallic state.

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Section: Finite-size Corrections To the Thermodynamic Bethe Ansatmentioning

confidence: 99%

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

Fujimoto

Kawakami

1998

J. Phys. A: Math. Gen.

126

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“…(7)). This is followed by a transformation of variables from k ± and λ ± to X r (r = c, s and X = ∆N, ∆D) evaluated at k ± = ±k 0 and λ ± = ±λ 0 , thereby incurring as the Jacobian matrix of the transformation a "dressed charge" matrix [20] which can be shown to obey the same integral equations with the unit matrix as inhomogeneity [20]. In our case, ξ is the function that parameterizes this matrix.…”

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confidence: 99%

Persistent currents through a quantum impurity: Protection through integrability

2007

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We consider an integrable model of a one-dimensional mesoscopic ring with the conduction electrons coupled by a spin exchange to a magnetic impurity. A symmetry analysis based on a Bethe Ansatz solution of the model reveals that the current is insensitive to the presence of the impurity. We argue that this is true for any integrable impurity-electron interaction, independent of choice of physical parameters or couplings. We propose a simple physical picture of how the persistent current gets protected by integrability.

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“…Given (7), the problem is now reduced to calculating how the excess numbers depend on the ABC fluxes in the presence of a Kondo dot. To do this, we apply the techniques of the Bethe ansatz for finite systems, developed previously for the 1D Hubbard model [21]. As we have already noted, our model is integrable for φ α = f α π, with f α an integer.…”

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confidence: 99%

Kondo Resonance in a Mesoscopic Ring Coupled to a Quantum Dot: Exact Results for the Aharonov-Bohm-Casher Effects

2001

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We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a side-branch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic AharonovBohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a current which, in the strong-coupling limit, is independent of the number of electrons in the ring. The Kondo effect-where the interaction between a local spin and free electrons produces a strongly-correlated state below a characteristic temperature T K -has become one of the paradigms in the study of correlated electron behavior [1]. In a recent experimental breakthrough [2], a tunable Kondo effect was observed in ultra small semiconductor quantum dots connected capacitively to a gate and via tunnel junctions to electrodes. By sweeping the gate voltage, the dot's highest spin-degenerate level ǫ d can be tuned relative to the chemical potential µ of the leads. This level is occupied by a single electron when) the oneparticle resonance width of the dot, and V k the tunneling matrix elements through the junction barriers. Below a temperature T K ∼ exp(−π|µ − ǫ d |/Γ d ) the resulting free spin on the dot forms a singlet with the electron spins in the leads via virtual co-tunneling processes. A fingerprint of this strongly correlated state is the dramatic enhancement of the local spectral density at the Fermi level. As predicted theoretically [3,4] and as seen in the experiments [2], this makes the dot transparent to electron transport when T ≪ T K .An interesting problem is how the persistent current (PC) of a multiply connected system coupled to a quantum dot is affected by a Kondo resonance. A PC is the equilibrium response [5][6][7] to a magnetic AharonovBohm (AB) flux [8] and/or an Aharonov-Casher "flux" [9] of a charged wire piercing the system. In contrast to ordinary (nonequilibrium) currents, as measured in the experiments referred to above, a PC requires for its existence that an electron maintains its phase coherence while circling the ring, and should thus be sensitive to scattering in the quantum dot [10]. The PC of a onedimensional (1D) ring coupled to a quantum dot was previously investigated by Büttiker and one of the authors [11], considering two different topologies: one in which the electron had to tunnel through the quantum dot in order to encircle the flux (embedded dot), and one in which an intact ring was coupled via a tunnel barrier to an adjacent quantum dot (sidebranch dot). However, in Ref.[11], the energy level spacing δ in the mesoscopic ring was taken to be much greater than T K , so that although a singlet state was formed between the electron on the dot and those within the ring, this state had more in common with a (tw...

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Finite-size corrections for the low lying states of a half-filled Hubbard chain

Cited by 75 publications

References 12 publications

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

Persistent currents through a quantum impurity: Protection through integrability

Kondo Resonance in a Mesoscopic Ring Coupled to a Quantum Dot: Exact Results for the Aharonov-Bohm-Casher Effects

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