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.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.

arXiv:1512.07908Nature CommunicationsAug 14, 2017120 citations

Quantum Critical Properties of the Bose-Fermi Kondo Model in a Large- N Limit

Lijun Zhu, Stefan Kirchner, Qimiao Si A +1 more

Studies of non-Fermi-liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large- $N$ approach to analyze an $\mathrm{S}\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{U}(\ensuremath{\kappa}N)$ generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-Ohmic spectrum ($|\ensuremath{\omega}{|}^{1\ensuremath{-}ϵ}\mathrm{s}\mathrm{g}\mathrm{n}\ensuremath{\omega}$, with $0<ϵ<1$ ). At the quantum-critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for $\ensuremath{\kappa}<1$) diverges. We also find an $\ensuremath{\omega}/T$ scaling for an extended range (15 decades) of $\ensuremath{\omega}/T$. This scaling violates (for $ϵ\ensuremath{\ge}1/2$) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.Studies of non-Fermi-liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-$N$ approach to analyze an $\mathrm{S}\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{U}(\ensuremath{\kappa}N)$ generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-Ohmic spectrum ($|\ensuremath{\omega}{|}^{1\ensuremath{-}ϵ}\mathrm{s}\mathrm{g}\mathrm{n}\ensuremath{\omega}$, with $0<ϵ<1$). At the quantum-critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for $\ensuremath{\kappa}<1$) diverges. We also find an $\ensuremath{\omega}/T$ scaling for an extended range (15 decades) of $\ensuremath{\omega}/T$. This scaling violates (for $ϵ\ensuremath{\ge}1/2$) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.

arXiv:cond-mat/0406293Physical Review LettersDec 21, 200461 citations

Spinless fermion model with quantum criticality

P. Schlottmann

Physica B Condensed MatterFeb 11, 20062 citations

Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

Bo-Hai Li, Zixiang Li, Hong Yao

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 ${Z}_{3}$ 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 $\mathrm{SU}(N$ ) 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 ${N}_{c}$ 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 $\mathrm{SU}(N$ ) 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 $N\ensuremath{\ge}1$.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 ${Z}_{3}$ 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 $\mathrm{SU}(N$) 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 ${N}_{c}$ 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 $\mathrm{SU}(N$) 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 $N\ensuremath{\ge}1$.

arXiv:1910.14287Physical review. B./Physical review. BFeb 5, 202013 citations

Deconfined quantum critical point in fermionic systems

Zixiang Li, Hong Yao

Bulletin of the American Physical SocietyMar 8, 20180 citations

Studies of non-Fermi-liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-

N

approach to analyze an $\mathrm{S}\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{U}(\ensuremath{\kappa}N)$ generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-Ohmic spectrum ($|\ensuremath{\omega}{|}^{1\ensuremath{-}ϵ}\mathrm{s}\mathrm{g}\mathrm{n}\ensuremath{\omega}$, with

0<ϵ<1

). At the quantum-critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for $\ensuremath{\kappa}<1$) diverges. We also find an $\ensuremath{\omega}/T$ scaling for an extended range (15 decades) of $\ensuremath{\omega}/T$. This scaling violates (for $ϵ\ensuremath{\ge}1/2$) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.

{Z}_{3}

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

\mathrm{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

{N}_{c}

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

\mathrm{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 $N\ensuremath{\ge}1$.