We consider interacting (2+1)-dimensional Dirac fermions with competing symmetry-breaking electronic instabilities, as described by relativistic quantum field theories of the Gross-Neveu-Yukawa flavor with anti-commuting mass terms. We demonstrate, using a combination of nonperturbative field-theoretical analysis and an adapted quantum Monte Carlo approach, that such systems exhibit a strong-coupling quantum multicritical fixed point with an emerging enhanced symmetry. Moreover, an extended phase coexistence regime expands out from this high-symmetry point. Our results disagree with recent results on the presence of a deconfined quantum criticality in (2+1)-dimensional Dirac fermions for the particular case of O(3) Neel and Z(2) Kekule symmetry-breaking instabilities on the graphene lattice. The robustness of these phenomena with respect to the microscopic symmetries furthermore demonstrates their relevance for a wide range of Dirac materials of current interest, from both theory and ongoing experiments.
Near the critical point of a phase transition, physical observables are characterized by a set of pure numbers -- the critical exponents -- which are identical for a whole class of transitions defining a ``universality class''. Novel Dirac materials exhibit quantum critical points, which are not captured by conventional universality classes and their description defines new challenges for theory. The authors present here a comprehensive renormalization group study and give quantitative predictions for universality classes of Dirac fermions, as relevant to semimetal-insulator transitions in graphene and emergent supersymmetry in topological insulators. The authors also compare to independent conformal bootstrap results and quantum Monte Carlo estimates.
This work deals with quantum phase transitions in Dirac systems where the symmetries involved play a key role in the nature of the transition and are enlarged at criticality. By using functional renormalization group (FRG) methods, we show that an emergent relativistic symmetry not present at the bare level is a common feature of several different kinds of phase transitions. In three different projects, the interplay of emergent symmetries and universality in critical phenomena are explored through FRG techniques. In the first project, we studied the relation between discrete symmetry breaking and the emergence of two diverging length scales with their respective critical exponents. A second project explored the relation between multicritical points where two adjacent symmetry-breaking phases are compatible and the possibility of a continuous, order-to-order transition. The third and final project was concerned with the persistence of chiral symmetry in three-dimensional quantum electrodynamics - here seen as an effective description of different condensed matter systems - for the lowest possible number of fermion flavours, as well as with a dual description that has the potential to provide exact results for this strongly correlated theory.
The recently discovered fermion-induced quantum critical points of Dirac materials present a new opportunity to revisit and extend the standard paradigms of quantum criticality. The appearance of a second diverging length scale at a continuous quantum phase transition is one such extension. The authors present a functional renormalization group study of fermion-induced quantum critical points in the broken-symmetry phase, in which the presence of gapless fermions and discrete symmetry breaking provide the natural setup for this phenomenon to occur.
We consider spontaneous symmetry-breaking transitions of strongly interacting two-dimensional Dirac fermions minimally coupled to mass and emergent gauge field order parameters. Using a renormalization group analysis, we show that the presence of gauge fields leads to fermion-induced quantum (multi)criticality where the putative emergent Lorentz invariance is violated. We illustrate this with the example of translational symmetry breaking due to charge-density wave order on the honeycomb lattice. Finally, we identify that topological phase transitions are well described by this effective field theory.
We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with
O(N1) and
O(N2) symmetries, respectively. Using $\ensuremath{\epsilon}$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent
O(N1+N2) symmetry for arbitrary values of
N1 and
N2 and fermion flavor numbers
Nf as long as the corresponding representation of the Clifford algebra exists. Small
O(N)-breaking perturbations near the chiral
O(N) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic
O(N) fixed point, which is stable only when
N<3. As a by-product, we obtain predictions for the critical behavior of the chiral
O(N) universality classes for arbitrary
N and fermion flavor number
Nf. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.