Confinement transition in the QED$_3$-Gross-Neveu-XY universality class

Abstract

The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of N f flavors of interacting Dirac fermions charged under a U(1) gauge field in 2+1 dimensions. Using Quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfined phase, described by three-dimensional quantum electrodynamics, and a gapped confined phase, in which the system develops valence-bond-solid order. We argue that the quantum critical point is in the universality class of the QED 3 -Gross-Neveu-XY model. We study this field theory within a 1/N f expansion in fixed dimension as well as a renormalization group analysis in 4 − space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.

Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

“…For small values of the gauge coupling, the numerical results are consistent with a gapless phase described by the deconfined, conformal QED 3 fixed point, which can be accessed either in the large-N f expansion [21][22][23][24][25] or in the expansion below four spacetime dimensions [26][27][28][29]. When the gauge coupling becomes strong, a quantum phase transition from the deconfined QED 3 phase to a confining phase occurs, accompanied by chiral symmetry breaking and dynamical mass generation for the fermions, and is found to be continuous [18][19][20]. For N f = 2, the confining phase is a Néel antiferromagnet.…”

“…By contrast, stronger effects of gauge fluctuations are expected to occur for lattice gauge theories with continuous gauge groups. Recently, sign-problem-free quantum Monte Carlo (QMC) simulations of a U (1) lattice gauge theory with an even number N f of flavors of fermions on the square lattice were performed [18][19][20]. At half filling, π magnetic flux is spontaneously generated in each plaquette-as in the Z 2 case-and Dirac fermions likewise emerge at low energies.…”

“…The chiral O(2) QED 3 -GNY model was also studied at oneloop order in the expansion in d = 4 − dimensions in Ref. [36], where a stable fixed point was found and critical exponents computed to O( ) [20].…”

“…We also improve upon existing one-loop results by computing critical exponents in the chiral O(2) QED 3 -GNY model at four-loop order in the expansion. In addition to our analytical results, we apply Padé and Padé-Borel resummation techniques to obtain numerical estimates of critical exponents in 2+1 dimensions for N f = 4, 6, 8, which pertain to the QMC studies mentioned earlier [18][19][20]. Finally, using both the large-N f and expansions we compute the CDW exponent ∆ CDW for the chiral O(2) GNY model, which character-izes the power-law decay of CDW correlations at the Kekulé VBS transition on the honeycomb lattice and is in principle accessible to QMC simulations such as those of Refs.…”

Deconfined criticality and ghost Fermi surfaces at the onset of antiferromagnetism in a metal

“…Starting from the FL* state, this transition is realized by turning on a M 2 condensate, while the Φ a condensate remains non-zero. Then, within the second hidden layer, the critical properties are described by a model considered earlier [37][38][39][40]: an O(3) QED 3 Gross-Neveu-Yukawa model. The spectator FL* Fermi surfaces could have a significant influence on this conformal field theory, but we will not explore this here.…”