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arXiv:1508.03078 · Physical review. B./Physical review. B

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

Nayana Shah, C. J. Bolech

Published Feb 29, 2016• 11 citations
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Abstract

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.

DOI
10.1103/physrevb.93.085440

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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.
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).
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.
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.