The chiral QED$_3$--Gross-Neveu-Yukawa (QED$_3$-GNY) theory is a $2+1$-dimensional U(1) gauge theory with $N_f$ flavors of four-component Dirac fermions coupled to a scalar field. For $N_f=1$, the specific chiral Ising QED$_3$-GNY model has recently been conjectured to be dual to the deconfined quantum critical point that describes Neel--valence-bond-solid transition of frustrated quantum magnets on square lattice. We study the universal critical behaviors of the chiral QED$_3$-GNY model in $d=4-ε$ dimensions for an arbitrary $N_f$ . We calculate the boson anomalous dimensions, inverse correlation length exponent, as well as the scaling dimensions of nonsinglet fermion bilinear in the chiral QED$_3$-GNY model. The Pad$\acute{e}$ estimates for the exponents are obtained in the chiral Ising-, XY- and Heisenberg-QED$_3$-GNY universality class respectively. We also establish the general condition of the supersymmetric criticality for the ungauged QED$_3$-GNY model. For the conjectured duality between chiral QED$_3$-GNY critical point and deconfined quantum critical point, we find the inverse correlation length exponent has a lower boundary $ν^{-1}>0.75$, beyond which the Ising-QED$_3$-GNY--$\mathbb{C}$P$^1$ duality may hold.
We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particula…
We calculate CFT data for the Gross-Neveu model in $2<d<4$ dimensions at the next-to-leading order in the $1/N$ expansion. In particular, we make use of the background field method to derive various conformal triangles involving the composite operator $s^2$, for the Hubbard-Stratonovich field $s$. We then apply these conformal triangles to obtain the corresponding OPE coefficients.
We use the critical point large $N$ formalism to calculate the critical exponents corresponding to the fermion mass operator and flavour non-singlet fermion bilinear operator in the universality class of Quantum Electrodynamics (QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in $d$-dimensions. The $ε$ expansion of the exponents in $d$ $=$ $4$ $-$ $2ε$ dimensions are in agreement with recent three and four loop perturbative evaluations of both renormalization group functions of these operators. Estimates of the value of the non-singlet operator exponent in three dimension…
Using analogies between flow equations from the Functional Renormalization Group and flow equations from (numerical) fluid dynamics we investigate the effects of bosonic fluctuations in a bosonized Gross-Neveu model -- namely the Gross-Neveu-Yukawa model. We study this model for finite numbers of fermions at varying chemical potential and temperature in the local potential approximation. Thereby we numerically demonstrate that for any finite number of fermions and as long as the temperature is non-zero, there is no $\mathbb{Z}_2$ symmetry breaking for arbitrary chemical potentials.
The Gross-Neveu model with ${\rm U}_L(N_f)\times{\rm U}_R(N_f)$ chiral symmetry is reconsidered in the large $N_c$ limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The ($x,t$)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.
The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade appr…
