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

arXiv:1508.03079 · Physical review. B./Physical review. B

Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point

C. J. Bolech, Nayana Shah

Published Feb 29, 2016• 18 citations
arXivHTMLPDF

Abstract

Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016)], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for nonequilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field, and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of interlead and intralead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.

DOI
10.1103/physrevb.93.085441

Related papers

Non-equilibrium transport in junctions using bosonization

Nayana Shah, C. J. Bolech

We will present our attempts to assure that bosonization-based calculations of non-equilibrium transport are fully consistent with the pre-bosonization formulations of the problems. Our initial focus on the case of a tunneling junction out of equilibrium showed that the conventional approach to bosonize-transform-debosonize gives results that are not consistent with the exact solution of that problem. We identified the root of the discrepancies in missing conservation laws and introduced a procedure that we developed to preserve these via a new framework that should be widely applicable [1]. We further applied the updated procedure to another key theoretical prototype of immediate experimental relevance, the two-lead Kondo junction [2]. Follow up calculations are helping to contextually demarcate when the need for the new bosonization framework arises in different types of problems. References: [1] Nayana Shah and C. J. Bolech, Phys. Rev. B  93 , 085440 (2016). [2] C. J. Bolech and Nayana Shah, Phys. Rev. B  93 , 085441 (2016).

StatPhys 27 Main Conference•Apr 17, 2019•0 citations

Systematic compactification of the two-channel Kondo model. I. Consistent bosonization-debosonization approach and exact comparisons

Aleksandar Ljepoja, C. J. Bolech, Nayana Shah

Capitalizing on recent work, which clarifies the consistent use of bosonization-debosonization methods to study Kondo-type quantum impurity models even in nonequilibrium settings, we revisit the compactification procedure of the two-channel Kondo model (by which it is rewritten more ``compactly'' using the single-channel version of the model and exploiting separation and duality between spin and charge) and uncover some hidden approximations that could limit its range of validity. This complements and extends, for two or any even number of channels, beyond previous work on the Toulouse limit of these models, and reinforces the need for the use of an extended framework in these calculations. We carry out a number of exact comparisons between the different models and show that keeping track of the so-called consistency factors leads to full agreement between the compactified and original versions of the model.

arXiv:2308.03569•Physical review. B./Physical review. B•Jul 8, 2024•3 citations

Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model

Adrian B. Culver, Natan Andrei

We present here the details of a method [A. B. Culver and N. Andrei, Many-body wavefunctions for quantum impurities out of equilibrium, Phys. Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals a universal regime of strong ferromagnetic coupling with Kondo temperature ${T}_{K}^{(F)}=D{e}^{\ensuremath{-}\frac{3{\ensuremath{\pi}}^{2}}{8}\ensuremath{\rho}|J|}$ ($J<0, \ensuremath{\rho}|J|\ensuremath{\rightarrow}\ensuremath{\infty}$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2{e}^{2}/h$ asymptotically at large voltage or temperature.

arXiv:1912.00281•Physical review. B./Physical review. B•May 4, 2021•5 citations

Transport through a correlated interface: Auxiliary master equation approach

Irakli Titvinidze, Antonius Dorda, Wolfgang von der Linden +1 more

We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, ${N}_{b}$ uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of ${N}_{b}$ than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.

arXiv:1508.02953•Physical Review B•Dec 21, 2015•24 citations

Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle

Nayana Shah, C. J. Bolech

We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.

arXiv:1508.03078•Physical review. B./Physical review. B•Feb 29, 2016•11 citations

Systematic compactification of the two-channel Kondo model. II. Comparative study of scaling and universality

Aleksandar Ljepoja, Nayana Shah, C. J. Bolech

Following up on the systematic compactification of the two-channel Kondo model [and its multichannel extensions; see Ljepoja et al., Phys. Rev. B 110, 045108 (2024)] and the demonstration of its validity over the past proposal of compactification, we resort to a study of scaling using Anderson's simple poor man's procedure to carry out a comparative study of these two and the original model. By doing so we unveil a universal agreement among the three models in how they flow upon scaling, and suggest the general limits of such a concordance. In this way we further elucidate the conditions under which the standard simplifications implicit in many bosonization-based mappings (particularly of quantum impurity models) can be used reliably, and when the consistent bosonization-debosonization approach is needed.

arXiv:2308.03590•Physical review. B./Physical review. B•Jul 8, 2024•3 citations
Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016)], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for nonequilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field, and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of interlead and intralead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.
We will present our attempts to assure that bosonization-based calculations of non-equilibrium transport are fully consistent with the pre-bosonization formulations of the problems. Our initial focus on the case of a tunneling junction out of equilibrium showed that the conventional approach to bosonize-transform-debosonize gives results that are not consistent with the exact solution of that problem. We identified the root of the discrepancies in missing conservation laws and introduced a procedure that we developed to preserve these via a new framework that should be widely applicable [1]. We further applied the updated procedure to another key theoretical prototype of immediate experimental relevance, the two-lead Kondo junction [2]. Follow up calculations are helping to contextually demarcate when the need for the new bosonization framework arises in different types of problems. References: [1] Nayana Shah and C. J. Bolech, Phys. Rev. B  93 , 085440 (2016). [2] C. J. Bolech and Nayana Shah, Phys. Rev. B  93 , 085441 (2016).
Capitalizing on recent work, which clarifies the consistent use of bosonization-debosonization methods to study Kondo-type quantum impurity models even in nonequilibrium settings, we revisit the compactification procedure of the two-channel Kondo model (by which it is rewritten more ``compactly'' using the single-channel version of the model and exploiting separation and duality between spin and charge) and uncover some hidden approximations that could limit its range of validity. This complements and extends, for two or any even number of channels, beyond previous work on the Toulouse limit of these models, and reinforces the need for the use of an extended framework in these calculations. We carry out a number of exact comparisons between the different models and show that keeping track of the so-called consistency factors leads to full agreement between the compactified and original versions of the model.
We present here the details of a method [A. B. Culver and N. Andrei, Many-body wavefunctions for quantum impurities out of equilibrium, Phys. Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at t=0t=0t=0. The method, which does not use Bethe ansatz, also works in other quantum impurity models and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals a universal regime of strong ferromagnetic coupling with Kondo temperature ${T}_{K}^{(F)}=D{e}^{\ensuremath{-}\frac{3{\ensuremath{\pi}}^{2}}{8}\ensuremath{\rho}|J|}$ ($J<0, \ensuremath{\rho}|J|\ensuremath{\rightarrow}\ensuremath{\infty}$). In this regime, the differential conductance dI/dVdI/dVdI/dV reaches the unitarity limit 2e2/h2{e}^{2}/h2e2/h asymptotically at large voltage or temperature.
We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, Nb{N}_{b}Nb​ uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of Nb{N}_{b}Nb​ than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.
We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.
Following up on the systematic compactification of the two-channel Kondo model [and its multichannel extensions; see Ljepoja et al., Phys. Rev. B 110, 045108 (2024)] and the demonstration of its validity over the past proposal of compactification, we resort to a study of scaling using Anderson's simple poor man's procedure to carry out a comparative study of these two and the original model. By doing so we unveil a universal agreement among the three models in how they flow upon scaling, and suggest the general limits of such a concordance. In this way we further elucidate the conditions under which the standard simplifications implicit in many bosonization-based mappings (particularly of quantum impurity models) can be used reliably, and when the consistent bosonization-debosonization approach is needed.