Fluctuations can change the phase transition properties drastically. An example is the fermion-induced quantum critical point (FIQCP), in which fluctuations of the massless Dirac fermions turn a putative Landau--de Gennes first-order phase transition (FOPT) with a cubic boson interaction into a continuous one. However, for the Landau-Devonshire theory, which characterizes another very large class of FOPTs, its fate under the coupling with extra fluctuations has not been explored. Here, we discover another type of FIQCP, in which the Dirac fermion fluctuations round the boson Landau-Devonshire FOPT into a continuous phase transition. By using the functional renormalization group analyses, we determine the condition for the appearance of this FIQCP. Moreover, we point out that the present FIQCP can be a supersymmetric critical point. We finally show that the low-temperature phase diagram can provide distinct experimental evidences to detect this FIQCP.
Fluctuations can change the phase transition properties drastically. An example is the fermion-induced quantum critical point (FIQCP), in which fluctuations of the massless Dirac fermions turn a putative Landau-de Gennes first-order phase transition (FOPT) with a cubic boson interaction into a continuous one. However, for the Landau-Devonshire theory, which characterizes another very large class of FOPTs, its fate under the coupling with extra fluctuations has not been explored. Here, we discover a new type of FIQCP, in which the Dirac fermion fluctuations round the boson Landau-Devonshire FOPT into a continuous phase transition. By using the functional renormalization group analyses, we determine the condition for the appearance of this FIQCP. Moreover, we point out that the present FIQCP can be a supersymmetric critical point. We finally show that the low-temperature phase diagram can provide distinct experimental evidences to detect this FIQCP.
According to the Landau criterion, a phase transition should be first order when cubic terms of order parameters are allowed in its effective Ginzburg-Landau free energy. Recently, it was shown by renormalization-group (RG) analysis that continuous transition can happen at putatively first-order
Z3 transitions in two-dimensional (2D) Dirac semimetals and such non-Landau phase transitions were dubbed ``fermion-induced quantum critical points'' (FIQCPs) [Z.-X. Li, Y.-F. Jiang, S.-K. Jian, and H. Yao, Nat. Commun. 8, 314 (2017)]. The RG analysis, controlled by the
1/N expansion with
N the number of flavors of four-component Dirac fermions, shows that the FIQCP occurs for $N\ensuremath{\ge}{N}_{c}$. Previous quantum Monte Carlo simulations of a microscopic model of
SU(N) fermions on the honeycomb lattice showed that the FIQCP occurs at the transition between Dirac semimetals and Kekule valence bond solids for $N\ensuremath{\ge}2$. However, the precise value of the lower bound
Nc has not been established. Especially, the case of
N=1 has not been explored by studying microscopic models so far. Here, by introducing a generalized
SU(N) fermion model with
N=1 (namely, spinless fermions on the honeycomb lattice), we perform large-scale sign-problem-free Majorana quantum Monte Carlo simulations and find convincing evidence of the FIQCP for
N=1. Consequently, our results suggest that the FIQCP can occur in 2D Dirac semimetals for all positive integers $N\ensuremath{\ge}1$.
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.
The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite-size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases, and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our results demonstrate that the interplay of massless Dirac fermions, critical fluctuations, and the finite-size effects could trigger a plethora of interesting phenomena, and therefore great care is called for when making generalizations.
In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and
Z3-ordered phases (e.g., Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first order. From large-
N renormalization-group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)] occur when
N (the number of flavors of four-component Dirac fermions) is larger than a critical value
Nc. Remarkably, from the knowledge of space-time supersymmetry, we obtain an exact lower bound for
Nc, i.e.,
Nc>1/2. (Here the ``1/2'' flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., $\ensuremath{\nu}\ensuremath{\ne}{\ensuremath{\nu}}^{\ensuremath{'}}$, by large-
N RG calculations. We further give a brief discussion of possible experimental realizations of FIQCPs.
Dynamical phase transition (DPT) characterizes the abrupt change in dynamical properties in nonequilibrium quantum many-body systems. It has been demonstrated that extra fluctuating modes besides the conventional order parameter field can bring about the Landau-forbidden quantum critical points by changing the order of the equilibrium phase transition. However, the counterpart phenomena in DPTs have rarely been explored. Here, we study the DPT in the Dirac system after a sudden quench and find that the fermion fluctuations can round a putative first-order DPT into a dynamical critical point, which is referred to as a fermion-induced dynamical critical point (FIDCP). This FIDCP gives the universal short-time scaling behavior controlled by the dynamical chiral fixed point despite the system going through a first-order transition after thermalization. In the novel scenario of FIDCP, the quantum Yukawa coupling
gq is indispensable for inducing the FIDCP even though it is irrelevant in the infrared scale. We call these variables dynamical dangerously irrelevant scaling variable. Moreover, a dynamical tricritical point which separates the first-order DPT and the FIDCP is discovered by tuning this dynamical dangerously irrelevant scaling variable. We further mention possible experimental realizations.