Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1609.03208 · Physical review. B./Physical review. B

Gauge-field-assisted Kekulé quantum criticality

Michael M. Scherer, Igor F. Herbut

Published Nov 23, 2016• 51 citations
arXivHTMLPDF

Abstract

We study the quantum phase transition of $U(1)$ charged Dirac fermions Yukawa coupled to the Kekul\'e valence-bond-solid order parameter with ${Z}_{3}$ symmetry of the honeycomb lattice. The symmetry allows for the presence of the term in the action which is cubic in the Kekul\'e order parameter and which is expected to prevent the quantum phase transition in question from being continuous. The Gross-Neveu-Yukawa theory for the transition is investigated using a perturbative renormalization group and within the $\ensuremath{\epsilon}$ expansion close to four space-time dimensions. For a vanishing $U(1)$ charge we show that quantum fluctuations may render the phase transition continuous only sufficiently far away from 3+1 dimensions, where the validity of the conclusions based on the leading-order $\ensuremath{\epsilon}$ expansion appears questionable. In the presence of a fluctuating gauge field, on the other hand, we find quantum critical behavior even at weak coupling to appear close to 3+1 dimensions, that is, within the domain of validity of the perturbation theory. We also determine the renormalization-group scaling of the cubic coupling at higher-loop orders and for a large number of Dirac fermions for vanishing charge.

DOI
10.1103/physrevb.94.205136

Related papers

Fermionic criticality with enlarged fluctuations in Dirac semimetals

Jiang Zhou, Su-Peng Kou

The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, we study the fermionic quantum criticality with enlarged Ising$\times$Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine the critical range in which the quantum fluctuations may render the phase transition continuous. We find that the Ising criticality is continuous only when the flavor numbers of four-component Dirac fermions $N_f\geq1/4$. Using the $ε$ expansion in four space-time dimensions, we then study the Ising$\times$Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising$\times$Ising Gross-Neveu-Yukawa universality class. Further, the correlation scaling behavior for the fermion bilinear on the honeycomb lattice at the multicritical point are also briefly discussed.

arXiv:2004.04085•Apr 8, 2020•0 citations

Fermionic multicriticality near Kekulé valence-bond ordering on a honeycomb lattice

Bitan Roy, Vladimir Juričić

We analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire a comparable propensity toward the nucleation of Kekul\'e valence-bond solid (KVBS) and charge-density-wave (${N}_{b}=1$) or $s$-wave pairing (${N}_{b}=2$) or antiferromagnet (${N}_{b}=3$) in a honeycomb lattice, where ${N}_{b}$ counts the number of bosonic order-parameter components. Besides the cubic terms present in the order-parameter description of KVBS due to the breaking of a discrete ${Z}_{3}$ symmetry, quantum fluctuations generate new cubic vertices near the high-symmetry MCPs. All cubic terms are strongly relevant at the bare level near three spatial dimensions, about which we perform a leading-order renormalization group analysis of coupled Gross-Neveu-Yukawa field theory. We show that due to nontrivial Yukawa interactions among gapless bosonic and fermionic degrees of freedom, all cubic terms ultimately become irrelevant at an $O(2+{N}_{b})$ symmetric MCP, at leas near two spatial dimensions, where ${N}_{b}=1,2,3$. Therefore, MCPs with an enlarged $O(2+{N}_{b})$ symmetry near KVBS ordering are stable.

arXiv:1902.08616•Physical review. B./Physical review. B•Jun 5, 2019•17 citations

Confinement transition in the QED3 -Gross-Neveu-XY universality class

Lukas Janssen, Wei Wang, Michael M. Scherer +2 more

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 ${N}_{\mathrm{f}}$ 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 ${\mathrm{QED}}_{3}$-Gross-Neveu-XY model. We study this field theory within a $1/{N}_{\mathrm{f}}$ expansion in fixed dimension as well as a renormalization group analysis in $4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.

arXiv:2003.01722•Physical review. B./Physical review. B•Jun 4, 2020•28 citations

Critical behavior of the QED3 -Gross-Neveu-Yukawa model at four loops

Nikolai Zerf, Peter Marquard, Rufus Boyack +1 more

We study the universal critical properties of the ${\mathrm{QED}}_{3}$-Gross-Neveu-Yukawa model with $N$ flavors of four-component Dirac fermions coupled to a real scalar order parameter at four-loop order in the $\ensuremath{\epsilon}$ expansion below four dimensions. For $N=1$, the model is conjectured to be infrared dual to the $\text{SU}(2)$-symmetric noncompact $\mathbb{C}{\mathrm{P}}^{1}$ model, which describes the deconfined quantum critical point of the N\'eel-valence-bond-solid transition of spin-1/2 quantum antiferromagnets on the two-dimensional square lattice. For $N=2$, the model describes a quantum phase transition between an algebraic spin liquid and a chiral spin liquid in the spin-1/2 kagome antiferromagnet. For general $N$ we determine the order-parameter anomalous dimension, the correlation length exponent, the stability critical exponent, as well as the scaling dimensions of $\text{SU}(N)$ singlet and adjoint fermion mass bilinears at the critical point. We use Pad\'e approximants to obtain estimates of critical properties in 2+1 dimensions.

arXiv:1808.00549•Physical review. B./Physical review. B•Oct 16, 2018•34 citations

Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach

Lukas Janssen, Igor F. Herbut

Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of onsite Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an $\mathrm{SO}(3)$ order parameter (``chiral Heisenberg universality class''). Our calculation yields an estimate of the critical exponents $\ensuremath{\nu}\ensuremath{\simeq}1.31$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}\ensuremath{\simeq}1.01$, and ${\ensuremath{\eta}}_{\ensuremath{\Psi}}\ensuremath{\simeq}0.08$, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method, we use the conventional Gross-Neveu-Yukawa theory with ${\mathbb{Z}}_{2}$ order parameter (``chiral Ising universality class'') as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in $2+1$ dimensions, our chiral Ising results agree with the best available predictions from other methods within the single-digit percent range for $\ensuremath{\nu}$ and ${\ensuremath{\eta}}_{\ensuremath{\phi}}$ and the double-digit percent range for ${\ensuremath{\eta}}_{\ensuremath{\Psi}}$. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented.

arXiv:1402.6277•Physical Review B•May 6, 2014•126 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 $N\ensuremath{\ge}1$.

arXiv:1910.14287•Physical review. B./Physical review. B•Feb 5, 2020•13 citations
We study the quantum phase transition of U(1)U(1)U(1) charged Dirac fermions Yukawa coupled to the Kekul'e valence-bond-solid order parameter with Z3{Z}_{3}Z3​ symmetry of the honeycomb lattice. The symmetry allows for the presence of the term in the action which is cubic in the Kekul'e order parameter and which is expected to prevent the quantum phase transition in question from being continuous. The Gross-Neveu-Yukawa theory for the transition is investigated using a perturbative renormalization group and within the \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ expansion close to four space-time dimensions. For a vanishing U(1)U(1)U(1) charge we show that quantum fluctuations may render the phase transition continuous only sufficiently far away from 3+1 dimensions, where the validity of the conclusions based on the leading-order \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ expansion appears questionable. In the presence of a fluctuating gauge field, on the other hand, we find quantum critical behavior even at weak coupling to appear close to 3+1 dimensions, that is, within the domain of validity of the perturbation theory. We also determine the renormalization-group scaling of the cubic coupling at higher-loop orders and for a large number of Dirac fermions for vanishing charge.
The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, we study the fermionic quantum criticality with enlarged Ising×\times×Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine the critical range in which the quantum fluctuations may render the phase transition continuous. We find that the Ising criticality is continuous only when the flavor numbers of four-component Dirac fermions Nf≥1/4N_f\geq1/4Nf​≥1/4. Using the εεε expansion in four space-time dimensions, we then study the Ising×\times×Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising×\times×Ising Gross-Neveu-Yukawa universality class. Further, the correlation scaling behavior for the fermion bilinear on the honeycomb lattice at the multicritical point are also briefly discussed.
We analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire a comparable propensity toward the nucleation of Kekul\'e valence-bond solid (KVBS) and charge-density-wave (Nb=1{N}_{b}=1Nb​=1) or sss-wave pairing (Nb=2{N}_{b}=2Nb​=2) or antiferromagnet (Nb=3{N}_{b}=3Nb​=3) in a honeycomb lattice, where Nb{N}_{b}Nb​ counts the number of bosonic order-parameter components. Besides the cubic terms present in the order-parameter description of KVBS due to the breaking of a discrete Z3{Z}_{3}Z3​ symmetry, quantum fluctuations generate new cubic vertices near the high-symmetry MCPs. All cubic terms are strongly relevant at the bare level near three spatial dimensions, about which we perform a leading-order renormalization group analysis of coupled Gross-Neveu-Yukawa field theory. We show that due to nontrivial Yukawa interactions among gapless bosonic and fermionic degrees of freedom, all cubic terms ultimately become irrelevant at an O(2+Nb)O(2+{N}_{b})O(2+Nb​) symmetric MCP, at leas near two spatial dimensions, where Nb=1,2,3{N}_{b}=1,2,3Nb​=1,2,3. Therefore, MCPs with an enlarged O(2+Nb)O(2+{N}_{b})O(2+Nb​) symmetry near KVBS ordering are stable.
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 Nf{N}_{\mathrm{f}}Nf​ flavors of interacting Dirac fermions charged under a U(1) gauge field in 2+12+12+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 QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu-XY model. We study this field theory within a 1/Nf1/{N}_{\mathrm{f}}1/Nf​ expansion in fixed dimension as well as a renormalization group analysis in $4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.
We study the universal critical properties of the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu-Yukawa model with NNN flavors of four-component Dirac fermions coupled to a real scalar order parameter at four-loop order in the $\ensuremath{\epsilon}$ expansion below four dimensions. For N=1N=1N=1, the model is conjectured to be infrared dual to the SU(2)\text{SU}(2)SU(2)-symmetric noncompact CP1\mathbb{C}{\mathrm{P}}^{1}CP1 model, which describes the deconfined quantum critical point of the N\'eel-valence-bond-solid transition of spin-1/2 quantum antiferromagnets on the two-dimensional square lattice. For N=2N=2N=2, the model describes a quantum phase transition between an algebraic spin liquid and a chiral spin liquid in the spin-1/2 kagome antiferromagnet. For general NNN we determine the order-parameter anomalous dimension, the correlation length exponent, the stability critical exponent, as well as the scaling dimensions of SU(N)\text{SU}(N)SU(N) singlet and adjoint fermion mass bilinears at the critical point. We use Pad\'e approximants to obtain estimates of critical properties in 2+1 dimensions.
Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of onsite Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3)\mathrm{SO}(3)SO(3) order parameter (``chiral Heisenberg universality class''). Our calculation yields an estimate of the critical exponents $\ensuremath{\nu}\ensuremath{\simeq}1.31$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}\ensuremath{\simeq}1.01$, and ${\ensuremath{\eta}}_{\ensuremath{\Psi}}\ensuremath{\simeq}0.08$, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method, we use the conventional Gross-Neveu-Yukawa theory with Z2{\mathbb{Z}}_{2}Z2​ order parameter (``chiral Ising universality class'') as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in 2+12+12+1 dimensions, our chiral Ising results agree with the best available predictions from other methods within the single-digit percent range for $\ensuremath{\nu}$ and ${\ensuremath{\eta}}_{\ensuremath{\phi}}$ and the double-digit percent range for ${\ensuremath{\eta}}_{\ensuremath{\Psi}}$. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented.
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{Z}_{3}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/N1/N1/N expansion with NNN 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\mathrm{SU}(NSU(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{N}_{c}Nc​ has not been established. Especially, the case of N=1N=1N=1 has not been explored by studying microscopic models so far. Here, by introducing a generalized SU(N\mathrm{SU}(NSU(N) fermion model with N=1N=1N=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=1N=1N=1. Consequently, our results suggest that the FIQCP can occur in 2D Dirac semimetals for all positive integers $N\ensuremath{\ge}1$.