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

• URL: http://arxiv.org/abs/2308.03569v2
• Date: Wed, 7 Aug 2024 18:59:56 GMT
• Title: Systematic compactification of the two-channel Kondo model. I. Consistent bosonization-debosonization approach and exact comparisons
• Authors: Aleksandar Ljepoja, C. J. Bolech, Nayana Shah,
• Abstract summary: We revisit the compactification procedure of the two-channel Kondo model. We uncover some hidden approximations that could limit its range of validity.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Capitalizing on recent work, that 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.

Related papers

• Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula [1.1970409518725493]
  Time-variant Sylvester-conjugate matrix equations are presented as early time-variant versions of the complex conjugate matrix equations. Current solving methods include Con-CZND1 and Con-CZND2 models, both of which use ode45 for continuous model. Based on Euler-forward formula discretion, Con-DZND1-2i model and Con-DZND2-2i model are proposed.
  arXiv  Detail & Related papers  (2024-11-04T17:58:31Z)
• Rectified Diffusion Guidance for Conditional Generation [62.00207951161297]
  We revisit the theory behind CFG and rigorously confirm that the improper configuration of the combination coefficients (i.e., the widely used summing-to-one version) brings about expectation shift of the generative distribution. We propose ReCFG with a relaxation on the guidance coefficients such that denoising with ReCFG strictly aligns with the diffusion theory. That way the rectified coefficients can be readily pre-computed via traversing the observed data, leaving the sampling speed barely affected.
  arXiv  Detail & Related papers  (2024-10-24T13:41:32Z)
• Systematic compactification of the two-channel Kondo model. III. Extended field-theoretic renormalization group analysis [44.99833362998488]
  We calculate the detailed flow for the (multi) two-channel Kondo model and its compactified versions. We gain insights into the contradistinction between the consistent vs. conventional bosonization-debosonization formalisms. In particular, we make use of renormalization-flow arguments to further justify the consistent refermionization of the parallel Kondo interaction.
  arXiv  Detail & Related papers  (2023-08-07T14:07:21Z)
• Systematic compactification of the two-channel Kondo model. II. Comparative study of scaling and universality [44.99833362998488]
  We study scaling using Anderson's simple poor man's procedure. We unveil a universal agreement among the three models in how they flow upon scaling.
  arXiv  Detail & Related papers  (2023-08-07T13:46:45Z)
• Understanding Parameter Sharing in Transformers [53.75988363281843]
  Previous work on Transformers has focused on sharing parameters in different layers, which can improve the performance of models with limited parameters by increasing model depth. We show that the success of this approach can be largely attributed to better convergence, with only a small part due to the increased model complexity. Experiments on 8 machine translation tasks show that our model achieves competitive performance with only half the model complexity of parameter sharing models.
  arXiv  Detail & Related papers  (2023-06-15T10:48:59Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning [78.30395044401321]
  We develop a novel model-based approach to reinforcement learning (MBRL) It relaxes the assumptions on the target transition model to belong to a generic family of mixture models. It can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
  arXiv  Detail & Related papers  (2022-06-02T17:27:49Z)
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices [0.0]
  Hermitian bipartite models are characterized by the presence of chiral symmetry and by Lieb's theorem. We introduce a class of non-Hermitian models with an arbitrary number of sublattices connected in a unidirectional and cyclical way.
  arXiv  Detail & Related papers  (2022-05-09T10:37:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.