arXiv subjects

T. A. Costi

Publications and source records attributed to T. A. Costi.

51 records · Page 3Linked to original sources

arXiv2003

Spectral function of the Kondo model in high magnetic fields

Using a recently developed perturbative renormalization group (RG) scheme, we calculate analytically the spectral function of a Kondo impurity for either large frequencies w or large magnetic field B and arbitrary frequencies. For large w >> max[B,T_K] the spectral function decays as 1/ln^2[ w/T_K ] with prefactors which depend on the magnetization. The spin-resolved spectral function displays a pronounced peak at w=B with a characteristic asymmetry. In a detailed comparison with results from numerical renormalization group (NRG) and bare perturbation theory in next-to-leading logarithmic order, we show that our perturbative RG scheme is controlled by the small parameter 1/ln[ max(w,B)/T_K]. Furthermore, we assess the ability of the NRG to resolve structures at finite frequencies.

cond-mat.str-el↗

arXiv2003

Mott transition and transport crossovers in the organic compound $κ-(BEDT-TTF)_2 Cu[N(CN)_2] Cl$

We have performed in-plane transport measurements on the two-dimensional organic salt $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl. A variable (gas) pressure technique allows for a detailed study of the changes in conductivity through the insulator-to-metal transition. We identify four different transport regimes as a function of pressure and temperature (corresponding to insulating, semi-conducting, ''bad metal'', and strongly correlated Fermi liquid behaviours). Marked hysteresis is found in the transition region, which displays complex physics that we attribute to strong spatial inhomogeneities. Away from the critical region, good agreement is found with a dynamical mean-field calculation of transport properties using the numerical renormalization group technique.

cond-mat.str-el↗

arXiv2002

Quantum fluctuations and electronic transport through strongly interacting quantum dots

We study electronic transport through a strongly interacting quantum dot by using the finite temperature extension of Wilson's numerical renormalization group (NRG) method. This allows the linear conductance to be calculated at all temperatures and in particular at very low temperature where quantum fluctuations and the Kondo effect strongly modify the transport. The quantum dot investigated has one active level for transport and is modeled by an Anderson impurity model attached to left and right electron reservoirs. The predictions for the linear conductance are compared to available experimental data for quantum dots in heterostructures. The spin-resolved conductance is calculated as a function of gate voltage, temperature and magnetic field strength and the spin-filtering properties of quantum dots in a magnetic field are described.

cond-mat.str-el↗

arXiv2001

Magnetic Correlations and the Anisotropic Kondo Effect in Ce1-xLaxAl3

By combining the results of muon spin rotation and inelastic neutron scattering in the heavy fermion compounds Ce1-xLaxAl3 (0.0 <= x <= 0.2), we show that static magnetic correlations are suppressed above a characteristic temperature, T*, by electronic dissipation rather than by thermal disorder. Below T*, an energy gap opens in the single-ion magnetic response in agreement with the predictions of the Anisotropic Kondo Model. Scaling arguments suggest that similar behavior may underlie the "hidden order" in URu2Si2.

cond-mat.str-el↗

arXiv2001

Magnetotransport through a strongly interacting quantum dot

We study the effect of a magnetic field on the conductance through a strongly interacting quantum dot by using the finite temperature extension of Wilson's numerical renormalization group method to dynamical quantities. The quantum dot has one active level for transport and is modelled by an Anderson impurity attached to left and right electron reservoirs. Detailed predictions are made for the linear conductance and the spin-resolved conductance as a function of gate voltage, temperature and magnetic field strength. A strongly coupled quantum dot in a magnetic field acts as a spin filter which can be tuned by varying the gate voltage. The largest spin-filtering effect is found in the range of gate voltages corresponding to the mixed valence regime of the Anderson impurity model.

cond-mat.mes-hall↗

arXiv2000

Finite temperature numerical renormalization group study of the Mott-transition

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T T_c there is a smooth crossover from metallic-like to insulating-like solutions.

cond-mat.str-el↗

arXiv2000

Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys

The effect of a magnetic field on the spectral density of a $\rm{S=1/2}$ Kondo impurity is investigated at zero and finite temperatures by using Wilson's numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value $H_{c}(T=0)\approx 0.5 T_{K}$, where $T_{K}$ is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on $\rm{Ce_{x}La_{1-x}Al_{2}}, x=0.0063$. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.

cond-mat.str-el↗

arXiv1999

Thermodynamics of the dissipative two-state system: a Bethe Ansatz study

The thermodynamics of the dissipative two-state system is calculated exactly for all temperatures and level asymmetries for the case of Ohmic dissipation. We exploit the equivalence of the two-state system to the anisotropic Kondo model and extract the thermodynamics of the former by solving the thermodynamic Bethe Ansatz equations of the latter. The universal scaling functions for the specific heat $C_α(T)$ and static dielectric susceptibility $χ_α(T)$ are extracted for all dissipation strengths $0<α<1$ for both symmetric and asymmetric two-state systems. The logarithmic corrections to these quantities at high temperatures are found in the Kondo limit $α\to 1^{-}$, whereas for $α< 1$ we find the expected power law temperature dependences with the powers being functions of the dissipative coupling $α$. The low temperature behaviour is always that of a Fermi liquid.

cond-mat.str-el↗

arXiv1998

Scaling and universality in the anisotropic Kondo model and the dissipative two-state system

Scaling and universality in the Ohmic two-state system is investigated by exploiting the equivalence of this model to the anisotropic Kondo model. For the Ohmic two-state system, we find universal scaling functions for the specific heat, $C_α(T)$, static susceptibility, $χ_α(T)$, and spin relaxation function $S_α(ω)$ depending on the reduced temperature $T/Δ_{r}$ (frequency $ω/Δ_{r}$), with $Δ_{r}$ the renormalized tunneling frequency, and uniquely specified by the dissipation strength $α$ ($0<α<1$). The scaling functions can be used to extract $α$ and $Δ_{r}$ in experimental realizations.

cond-mat.str-el↗

arXiv1997

Renormalization Group Approach to Non-equilibrium Green Functions in Correlated Impurity Systems

We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state problems, which correspond to the situations before and after the disturbance (an electric or magnetic field, for example) is suddenly switched on, are solved with the aid of Wilson's momentum shell renormalization group. The method is illustrated by calculating the non-equilibrium dynamics of the ohmic two-state problem.

cond-mat.str-el↗

arXiv1997

Unified description of Fermi and non-Fermi liquid behavior in a conserving slave boson approximation for strongly correlated impurity models

We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the Kondo limit the bound state contributions are unimportant.

cond-mat.str-el↗

arXiv1996

Equilibrium dynamics of the dissipative two-state system

Wilson's momentum shell renormalization group method is used to solve for the dynamics of the dissipative two--state system. We utilize the mapping of the spin--boson model onto the anisotropic Kondo model (AKM) and solve for the dynamics of the latter. We find that the AKM captures the physics of the dissipative two--state system for dissipation strength $0\leqα\leq 4$ corresponding to $\infty\geq J_{\parallel}\geq -\infty$ in the AKM. The dynamics of the AKM shows a smooth crossover between two strong coupling regimes corresponding to weak and strong dissipation in the spin--boson model.

cond-mat↗

arXiv1995

Spectral Properties of the Anderson Impurity Model, Comparison of Numerical Renormalization Group and Non--Crossing Approximation

A comparative study of the numerical renormalization group and non-crossing approximation results for the spectral functions of the $U=\infty$ Anderson impurity model is carried out. The non-crossing approximation is the simplest conserving approximation and has led to useful insights into strongly correlated models of magnetic impurities. At low energies and temperatures the method is known to be inaccurate for dynamical properties due to the appearance of singularities in the physical Green's functions. The problems in developing alternative reliable theories for dynamical properties have made it difficult to quantify these inaccuracies. As a first step in obtaining a theory which is valid also in the low energy regime, we identify the origin of the problems within the NCA. We show, by comparison with close to exact NRG calculations for the auxiliary and physical particle spectral functions, that the main source of error in the NCA is in the lack of vertex corrections in the convolution formulae for physical Green's functions. We show that the dynamics of the auxiliary particles within NCA is essentially correct for a large parameter region, including the physically interesting Kondo regime, for all energy scales down to $T_{0}$, the low energy scale of the model, and often well below this scale. Despite the satisfactory description of the auxiliary particle dynamics, the physical spectral functions are not obtained accurately on scales $\sim T_{0}$. Our results suggest that self--consistent conserving approximations which include vertex terms may provide a highly accurate way of dealing with strongly correlated systems at low temperatures.

cond-mat↗

arXiv1994

Numerical Renormalization Group Study of Pseudo-Fermion and Slave-Boson Spectral Functions in the Single Impurity Anderson Model

We use the numerical renormalization group to calculate the auxiliary spectral functions of the $U=\infty$ Anderson impurity model. The slave--boson and pseudo--fermion spectral functions diverge at the threshold with exponents $α_{b}$ and $α_{f}$ given in terms of the conduction electron phase shifts by the X--ray photoemission and the X--ray absorption exponents respectively. The exact exponents obtained here depend on the impurity occupation number, in contrast to the NCA results. Vertex corrections in the convolution formulae for physical Green's functions are singular at the threshold and may not be neglected in the Fermi liquid regime.

cond-mat↗

arXiv1993

Transport Coefficients of the Anderson Model via the Numerical Renormalization Group

The transport coefficients of the Anderson model are calculated by extending Wilson's NRG method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single--particle spectral densities and transport time $τ(ω,T)$ are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit. The low temperature anomalies in the resistivity, $ρ(T)$, thermopower, $S(T)$, thermal conductivity $κ(T)$ and Hall coefficient, $R_{H}(T)$, are discussed. All quantities exhibit the expected Fermi liquid behaviour at low temperature with power law dependecies on $T/T_{K}$ in very good agreement with analytic results based on Fermi liquid theory. Scattering of conduction electrons in higher, $l>0$, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of non--resonant scattering on the transport properties.

cond-mat↗