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}
}
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… Expand

Figures from this paper

Testing the Bethe ansatz with large N renormalons
The ground-state energy of integrable asymptotically free theories can be conjecturally computed using the Bethe ansatz once the theory has been coupled to an external potential through a conservedExpand
Resurgence and 1/N Expansion in Integrable Field Theories
Abstract In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for theExpand
Quantum phase transition and Resurgence: Lessons from 3d N = 4 SQED
We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional N = 4Expand
Analytic resurgence in the O(4) model
We study the perturbative expansion of the ground state energy in the presence of an external field coupled to a conserved charge in the integrable two-dimensional O(4) nonlinear sigma model. ByExpand
Resurgence and renormalons in the one-dimensional Hubbard model
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, weExpand

References

SHOWING 1-10 OF 56 REFERENCES
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
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 energyExpand
Exact Perturbative Results for the Lieb–Liniger and Gaudin–Yang Models
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. ThisExpand
Yang―Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
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 theExpand
Mott transition in the one-dimensional SU (n) Hubbard model
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 inExpand
Resurgence for superconductors
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 beExpand
Exact studies of ground and excited states of one-dimensional δ-interacting Fermi gases in the BCS–BEC crossover
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 ofExpand
Effective Field Theory for Fermi Systems in a Large N Expansion
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 auxiliaryExpand
Exactly solvable model of the BCS-BEC crossover.
TLDR
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. Expand
Resurgence for superconductors
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 beExpand
The Fermi gas model of one-dimensional conductors
Abstract The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model,Expand
...
1
2
3
4
5
...