Lattice investigation of an inhomogeneous phase of the 2 + 1-dimensional Gross-Neveu model in the limit of infinitely many flavors

Abstract

We investigate the phase structure of the 2 + 1 dimensional Gross-Neveu model in the large-Nf limit, where Nf denotes the number of fermion flavors. We discuss two different fermion representations and their implication on the interpretation of a discrete symmetry of the action. We present numerical results, which indicate the existence of an inhomogeneous phase similar as in the 1+1-dimensional Gross-Neveu model.

Inhomogeneous Phases in the Chirally Imbalanced 2 + 1-Dimensional Gross-Neveu Model and Their Absence in the Continuum Limit

“…In the plots in the left column, however, there are pronounced oscillations that seem to be caused by small spatial volume. These oscillations are reminiscent of those observed in the µ-T plane in lattice studies of the chirally balanced GN model in 1 + 1 and 2 + 1 dimensions [31,33,67].…”

“…Using lattice field theory the phase diagram of the 2 + 1-dimensional GN model with µ 45 = 0 was extensively explored in refs. [31][32][33]. There is a symmetric phase with σ = 0 at large µ or large T and a homogeneous symmetry-broken phase with a constant σ = σ at small µ and small T. Moreover, at finite lattice spacing and for certain discretizations (e.g., W2 = W 2 ) there is additionally an inhomogeneous phase, where σ(x) is a varying function of the spatial coordinates.…”

“…Recently, the existence of inhomogeneous phases was also explored in the 2 + 1dimensional GN model in the mean-field approximation [31][32][33]. Such 2 + 1-dimensional four-fermion theories are of interest both in high energy physics [34][35][36][37][38] and in condensed matter physics [39][40][41][42][43][44][45][46], but also to study conceptual questions, e.g., renormalizability in the 1/N expansion or in a perturbative approach [47][48][49][50].…”

Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit

“…Recently, the existence of inhomogeneous phases was also explored in the 2 + 1dimensional GN model in the mean-field approximation [27][28][29]. Such 2 + 1-dimensional four-fermion theories are of interest both in high energy physics [30][31][32][33][34] and in condensed matter physics [35][36][37][38][39][40][41][42], but also to study conceptual questions, e.g., renormalizability in the 1/N expansion or in a perturbative approach [43][44][45][46].…”

Cascade of phase transitions in a planar Dirac material

“…They appear in some condensed matter systems [10][11][12][13][14][15][16][17][18][19][20] and understanding the effects of interactions is therefore imperative. Historically, four-fermion models of Dirac fermions in 2 + 1 dimensions have been thoroughly studied both analytically [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and by numerical simulations [37][38][39][40][41][42][43][44], and intriguing features such as superfluidity, Kosterlitz-Thouless transitions, non-Gaussian Ultra-Violet (UV) fixed points and magnetic catalysis have been elucidated. These studies have provided a tractable avenue for understanding nonperturbative aspects of (2 + 1)-dimensional strongly coupled gauge theories, including QED 3 and QCD 3 as prominent examples.…”