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

Exact results in the Interacting Resonant Level Model

Gonzalo Camacho

Published Dec 1, 2017• 1 citation
OpenAlex

Abstract

The Interacting Resonant Level Model (IRLM) is studied by making use of different standard techniques common to the study strongly correlated quantum systems. Exact results are computed both analytically and numerically, in order to obtain a full consistent theory of the model in equilibrium thermodynamics, opening the path towards a future treatment of the model.

Related papers

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

Annamária Kiss, Junya Otsuki, Yoshio Kuramoto

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction Ufc and hybridization V. Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V. For negative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.

arXiv:1308.1209•Journal of the Physical Society of Japan•Nov 20, 2013•4 citations

Exact thermodynamics in the Interacting Resonant Level Model

Gonzalo Camacho, Peter Schmitteckert, Sam T. Carr

We present exact results for the thermodynamic properties of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale $T_K$ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level model does not correctly reproduce $T_K$ - however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.

•Jan 1, 2018•0 citations

Scaling theory vs exact numerical results for spinless resonant level model

Kiss, Annamária, Junya Otsuki, Yoshio Kuramoto

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) \nusing double expansion with respect to Coulomb interaction Ufc and hybridization V . Thermodynamics of the \nIRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and \nthermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V . For \nnegative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that \ndeals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order \nscaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain \nSamarium compounds with unusual heavy-fermion behavior.

•Jan 1, 2013•4 citations

Infrared expansion of entanglement entropy in the interacting resonant level model

L. Freton, E. Boulat, Hubert Saleur

In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the Interacting Resonant Level Model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infrared fixed point, conformal field theory techniques initially developed by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/TB in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.

arXiv:1301.6535•Nuclear Physics B•May 28, 2013•15 citations

From thermal equilibrium to nonequilibrium quench dynamics: A conserving approximation for the interacting resonant level

Yuval Vinkler-Aviv, Avraham Schiller, Frithjof B. Anders

We develop a low-order conserving approximation for the interacting resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii) nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal equilibrium is first used to carefully gauge the quality of the approximation by comparing the results with other well-studied methods, and finding good agreement for small values of the interaction. We analytically show that the power-law exponent of the renormalized level width usually derived using renormalization group approaches can also be correctly obtained in our approach in the weak interaction limit. A closed expression for the nonequilibrium steady-state current is derived and analytically and numerically evaluated. We find a negative differential conductance at large voltages, and the exponent of the power-law suppression of the steady-state current is calculated analytically at zero temperature. The response of the system to quenches is investigated for a single lead as well as for two-lead setup at finite voltage bias at particle-hole symmetry using a self-consistent two-times Keldysh Green function approach, and results are presented for the time-dependent current for different bias and contact interaction strength.

arXiv:1406.0254•Physical Review B•Oct 8, 2014•14 citations

Exact equilibrium results in the interacting resonant level model

Gonzalo Camacho, Peter Schmitteckert, Sam T. Carr

We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the numerical renormalization group and density matrix renormalization group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale ${T}_{K}$ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce ${T}_{K}$---however, if the bare parameters in the model are renormalized, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.

arXiv:1810.08246•Physical review. B./Physical review. B•Feb 12, 2019•14 citations
The Interacting Resonant Level Model (IRLM) is studied by making use of different standard techniques common to the study strongly correlated quantum systems. Exact results are computed both analytically and numerically, in order to obtain a full consistent theory of the model in equilibrium thermodynamics, opening the path towards a future treatment of the model.
The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction Ufc and hybridization V. Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V. For negative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.
We present exact results for the thermodynamic properties of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale TKT_KTK​ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level model does not correctly reproduce TKT_KTK​ - however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.
The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) \nusing double expansion with respect to Coulomb interaction Ufc and hybridization V . Thermodynamics of the \nIRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and \nthermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V . For \nnegative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that \ndeals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order \nscaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain \nSamarium compounds with unusual heavy-fermion behavior.
In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the Interacting Resonant Level Model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infrared fixed point, conformal field theory techniques initially developed by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/TB in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.
We develop a low-order conserving approximation for the interacting resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii) nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal equilibrium is first used to carefully gauge the quality of the approximation by comparing the results with other well-studied methods, and finding good agreement for small values of the interaction. We analytically show that the power-law exponent of the renormalized level width usually derived using renormalization group approaches can also be correctly obtained in our approach in the weak interaction limit. A closed expression for the nonequilibrium steady-state current is derived and analytically and numerically evaluated. We find a negative differential conductance at large voltages, and the exponent of the power-law suppression of the steady-state current is calculated analytically at zero temperature. The response of the system to quenches is investigated for a single lead as well as for two-lead setup at finite voltage bias at particle-hole symmetry using a self-consistent two-times Keldysh Green function approach, and results are presented for the time-dependent current for different bias and contact interaction strength.
We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the numerical renormalization group and density matrix renormalization group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale TK{T}_{K}TK​ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce TK{T}_{K}TK​---however, if the bare parameters in the model are renormalized, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.