Bounded particle interactions driven by a nonlocal dual Chern-Simons model

Abstract

Quantum electrodynamics (QED) of electrons confined in a plane and that yet can undergo interactions mediated by an unconstrained photon has been described by the so-called pseudo-QED (PQED), the (2+1)-dimensional version of the equivalent dimensionally reduced original QED. In this work, we show that PQED with a nonlocal Chern-Simons term is dual to the Chern-Simons Higgs model at the quantum level. We apply the path-integral formalism in the dualization of the Chern-Simons Higgs model to first describe the interaction between quantum vortex particle excitations in the dual model. This interaction is explicitly shown to be in the form of a Bessel-like type of potential in the static limit. This result per se opens exciting possibilities for investigating topological states of matter generated by interactions, since the main difference between our new model and the PQED is the presence of a nonlocal Chern-Simons action. Indeed, the dual transformation yields an unexpected square root of the d'Alembertian operator, namely, ( √ − ) −1 multiplied by the well-known Chern-Simons action. Despite the nonlocality, the resulting model is still gauge invariant and preserves the unitarity, as we explicitly prove. Finally, when coupling the resulting model to Dirac fermions, we then show that pairs of bounded electrons are expected to appear, with a typical distance between the particles being inversely proportional to the topologically generated mass for the gauge field in the dual model.

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

“…The other functions, f 1 ðλÞ and f 2 ðλÞ, are similarly obtained from the angular integrals in Eqs. (17) and (18) as in Ref. [23].…”

“…Therefore, the renormalization of v F is straightforward within this quantum-electrodynamical approach. Indeed, in similar systems, the use of quantum field theory techniques has been shown very useful for describing electronic properties in both perturbative [4,5,[13][14][15][16][17][18][19][20][21] and nonperturbative [6][7][8][22][23][24][25][26] approaches. In particular, the random phase approximation (RPA), which is equivalent to leading order in the 1=N approximation [6], has been used in the description of some properties of suspended [8,26] and doped [25,27,28] graphene.…”

Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane

“…This action has been shown dual to the Chern-Simons-Higgs model in Ref. [96]), using standard path-integral formalism. When coupled to PQED, we find a Euclidean action, given by…”

“…This CS parameter, however, is dimensionless and can not generate a mass for the gauge field in PQED. In order to do so, one has to consider the Pseudo Chern-Simons (PCS) action, obtained by dual transformation of an abelian CS-Higgs [96] or by a bosonization of massive Dirac fermions [97]. We shall refer as Pseudo Maxwell-Chern-Simons (PMCS) to the model that combines PQED and PCS; this PMCS has a peculiar feature of producing bound states of electrons [96,97].…”

“…In order to do so, one has to consider the Pseudo Chern-Simons (PCS) action, obtained by dual transformation of an abelian CS-Higgs [96] or by a bosonization of massive Dirac fermions [97]. We shall refer as Pseudo Maxwell-Chern-Simons (PMCS) to the model that combines PQED and PCS; this PMCS has a peculiar feature of producing bound states of electrons [96,97]. Nevertheless, effects of dynamical mass generation had not been investigated for the PMCS until now.…”