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:1708.02256 · Physical review. B./Physical review. B

Critical behavior of the QED3 -Gross-Neveu model: Duality and deconfined criticality

Lukas Janssen, Yin-Chen He

Published Nov 8, 2017• 46 citations
arXivHTMLPDF

Abstract

We study the critical properties of the ${\mathrm{QED}}_{3}$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to the SU(2) noncompact ${\mathrm{CP}}^{1}$ model that describes the deconfined phase transition between the N\'eel antiferromagnet and the valence bond solid on the square lattice. For $N=2$, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-$1/2$ systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the ${\mathrm{QED}}_{3}$-Gross-Neveu model for all values of $N$. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain ${\mathrm{QED}}_{3}$ (without scalar-field coupling) unstable at low values of $N$. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $\ensuremath{\epsilon}=4\ensuremath{-}D$. We compute the scalar-field anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, the correlation-length exponent $\ensuremath{\nu}$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{z}\ensuremath{\psi}$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

DOI
10.1103/physrevb.96.205113

Related papers

Deconfined criticality in the QED3 Gross-Neveu-Yukawa model: The 1/N expansion revisited

Rufus Boyack, Ahmed Rayyan, Joseph Maciejko

The critical properties of the ${\mathrm{QED}}_{3}$ Gross-Neveu-Yukawa (GNY) model in 2 + 1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the N\'eel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $\ensuremath{\epsilon}$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the ${\mathrm{QED}}_{3}$ GNY critical point are in reasonable agreement with numerical studies of the N\'eel-to-VBS transition, in support of the duality conjecture.

arXiv:1812.02720•Physical review. B./Physical review. B•May 20, 2019•35 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

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

Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets

Flavio S. Nogueira

Quantum electrodynamics in $2+1$ dimensions is an effective gauge theory for the so-called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul et al., Nat. Phys. 4, 28 (2008)]. In this context, by using the renormalization group in $d=4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions, we show that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species ${N}_{f}\ensuremath{\ge}4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of ${N}_{f}$. In particular, for ${N}_{f}=4$ and $\ensuremath{\epsilon}=1$ $(d=2+1)$, the anomalous dimension of the N\'eel field is given by ${\ensuremath{\eta}}_{N}=1/3$, with a correlation length exponent $\ensuremath{\nu}=1/2$. These values considerably change for ${N}_{f}>4$. For instance, for ${N}_{f}=6$, we find ${\ensuremath{\eta}}_{N}\ensuremath{\approx}0.75\text{ }191$ and $\ensuremath{\nu}\ensuremath{\approx}0.660\text{ }09$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, ${G}_{\ensuremath{\chi}}(x)\ensuremath{\equiv}⟨\overline{\ensuremath{\psi}}(x)\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0)\ensuremath{\psi}(0)⟩$.

arXiv:0802.0500•Physical Review B•May 5, 2008•8 citations

Deconfined criticality and a gapless Z 2 spin liquid in the square-lattice antiferromagnet

Henry Shackleton, Alex Thomson, Subir Sachdev A

The theory for the vanishing of N\'eel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable ${\mathbb{Z}}_{2}$ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless ${\mathbb{Z}}_{2}$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing ${J}_{2}/{J}_{1}$: N\'eel, gapless ${\mathbb{Z}}_{2}$ spin liquid, and valence bond solid.

arXiv:2104.09537•Physical review. B./Physical review. B•Jul 6, 2021•27 citations

Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities

Yuan Da Liao, Xiao Yan Xu, Zi Yang Meng +1 more

We investigate the ground state phase diagram of an extended Hubbard model with a $\ensuremath{\pi}$-flux hopping term at half filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents ${\ensuremath{\eta}}_{\text{VBS}}=0.6(1)$ and ${\ensuremath{\eta}}_{\text{AFM}}=0.58(3)$ at a deconfined quantum critical point satisfy the conformal field theory bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and closed at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum moir\'e systems, are discussed.

arXiv:2204.04884•Physical review. B./Physical review. B•Aug 4, 2022•22 citations
We study the critical properties of the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu model with 2N2N2N flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N=1N=1N=1, this theory has recently been suggested to be dual to the SU(2) noncompact CP1{\mathrm{CP}}^{1}CP1 model that describes the deconfined phase transition between the N'eel antiferromagnet and the valence bond solid on the square lattice. For N=2N=2N=2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/21/21/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu model for all values of NNN. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3{\mathrm{QED}}_{3}QED3​ (without scalar-field coupling) unstable at low values of NNN. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter \ensuremathϵ=4\ensuremath−D\ensuremath{\epsilon}=4\ensuremath{-}D\ensuremathϵ=4\ensuremath−D. We compute the scalar-field anomalous dimension \ensuremathη\ensuremathϕ{\ensuremath{\eta}}_{\ensuremath{\phi}}\ensuremathη\ensuremathϕ​, the correlation-length exponent \ensuremathν\ensuremath{\nu}\ensuremathν, as well as the scaling dimension of the flavor-symmetry-breaking bilinear \ensuremathψ‾\ensuremathσz\ensuremathψ\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{z}\ensuremath{\psi}\ensuremathψ​\ensuremathσz\ensuremathψ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.
The critical properties of the QED3{\mathrm{QED}}_{3}QED3​ Gross-Neveu-Yukawa (GNY) model in 2 + 1 dimensions with NNN flavors of two-component Dirac fermions are computed to first order in the 1/N1/N1/N expansion. For the specific case of N=2N=2N=2, the critical point is conjectured to be dual to the N\'eel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $\ensuremath{\epsilon}$- and 1/N1/N1/N-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED3{\mathrm{QED}}_{3}QED3​ GNY critical point are in reasonable agreement with numerical studies of the N\'eel-to-VBS transition, in support of the duality conjecture.
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.
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.
Quantum electrodynamics in 2+12+12+1 dimensions is an effective gauge theory for the so-called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul et al., Nat. Phys. 4, 28 (2008)]. In this context, by using the renormalization group in $d=4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions, we show that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species ${N}_{f}\ensuremath{\ge}4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of Nf{N}_{f}Nf​. In particular, for Nf=4{N}_{f}=4Nf​=4 and $\ensuremath{\epsilon}=1$ (d=2+1)(d=2+1)(d=2+1), the anomalous dimension of the N\'eel field is given by ${\ensuremath{\eta}}_{N}=1/3$, with a correlation length exponent $\ensuremath{\nu}=1/2$. These values considerably change for Nf>4{N}_{f}>4Nf​>4. For instance, for Nf=6{N}_{f}=6Nf​=6, we find ${\ensuremath{\eta}}_{N}\ensuremath{\approx}0.75\text{ }191$ and $\ensuremath{\nu}\ensuremath{\approx}0.660\text{ }09$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, ${G}_{\ensuremath{\chi}}(x)\ensuremath{\equiv}⟨\overline{\ensuremath{\psi}}(x)\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0)\ensuremath{\psi}(0)⟩$.
The theory for the vanishing of N\'eel order in the spin S=1/2S=1/2S=1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z2{\mathbb{Z}}_{2}Z2​ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J2/J1{J}_{2}/{J}_{1}J2​/J1​: N\'eel, gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid, and valence bond solid.
We investigate the ground state phase diagram of an extended Hubbard model with a $\ensuremath{\pi}$-flux hopping term at half filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents ${\ensuremath{\eta}}_{\text{VBS}}=0.6(1)$ and ${\ensuremath{\eta}}_{\text{AFM}}=0.58(3)$ at a deconfined quantum critical point satisfy the conformal field theory bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and closed at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum moir\'e systems, are discussed.