• Corpus ID: 226221747

# Three roads to the energy gap

@article{Mario2020ThreeRT,
title={Three roads to the energy gap},
author={Marcos Mari{\~n}o and Tom{\'a}s Reis},
journal={arXiv: High Energy Physics - Theory},
year={2020}
}
• Published 30 October 2020
• Physics, Mathematics
• arXiv: High Energy Physics - Theory
We determine analytically the energy gap at weak coupling in the attractive multi-component Gaudin--Yang model, an integrable model which describes interacting fermions in one dimension with $\kappa$ components. We use three different methods. The first one is based on a direct analysis of the Bethe ansatz equations. The second method uses the theory of resurgence and the large order behavior of the perturbative series for the ground state energy. The third method is based on a renormalization…
5 Citations

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## References

SHOWING 1-10 OF 56 REFERENCES
Resurgence and renormalons in the one-dimensional Hubbard model
• Physics, Mathematics
• 2020
We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we
Application of the renormalization group technique to the problem of phase transition in one-dimensional metallic systems. I. Invariant couplings, vertex, and one-particle Green's function
• Physics
• 1973
A one-dimensional system of electrons interacting via a BCS-type interaction is investigated by renormalization group techniques in two successive approximations atT=0, keeping only a single energy
Exact Perturbative Results for the Lieb–Liniger and Gaudin–Yang Models
• Physics, Mathematics
Journal of Statistical Physics
• 2019
We present a systematic procedure to extract the perturbative series for the ground state energy density in the Lieb-Liniger and Gaudin-Yang models, starting from the Bethe ansatz solution. This
Yang―Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
• Physics, Mathematics
• 2011
Using Yang and Yang's particle–hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general SU(κ) fermionic system in one dimension for both the
Mott transition in the one-dimensional SU (n) Hubbard model
• Physics
• 2005
The one-dimensional SU$(n)$ Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for $ng2$. It is found that in
Resurgence for superconductors
• Physics
• 2019
An important non-perturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can be
Exact studies of ground and excited states of one-dimensional δ-interacting Fermi gases in the BCS–BEC crossover
• Physics
• 2012
We propose an eigenfunction expansion method to solve the integral equations raised by one-dimensional δ-interaction integrable models. Based on this method, the crossover from BCS superfluid of
Effective Field Theory for Fermi Systems in a Large N Expansion
• Physics
• 2002
Abstract A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary
Exactly solvable model of the BCS-BEC crossover.
• Medicine, Physics
Physical review letters
• 2004
An integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid is discussed and an experimental realization with cold atoms of such a one-dimensional B CS-BEC crossover is proposed.
Resurgence for superconductors
• Physics, Mathematics
• 2019
An important non-perturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can be