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:2003.01722 · Physical review. B./Physical review. B

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

Lukas Janssen, Wei Wang, Michael M. Scherer, Zi Yang Meng, Xiao Yan Xu

Published Jun 4, 2020• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.101.235118

Related papers

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

Lukas Janssen, Yin-Chen He

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.

arXiv:1708.02256•Physical review. B./Physical review. B•Nov 8, 2017•46 citations

Dynamics of compact quantum electrodynamics at large fermion flavor

Wei Wang, Da-Chuan Lu, Xiao Yan Xu +2 more

Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at ($2+1$)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (${N}_{f}$) and the strength of gauge fluctuations is mapped out. Here we focus on the large fermion flavor case (${N}_{f}=8$) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the ${\mathrm{QED}}_{3}$-Gross-Neveu chiral O(2) universality whose properties are still largely unknown.

arXiv:1906.06929•Physical review. B./Physical review. B•Aug 13, 2019•28 citations

Gauge-field-assisted Kekulé quantum criticality

Michael M. Scherer, Igor F. Herbut

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.

arXiv:1609.03208•Physical review. B./Physical review. B•Nov 23, 2016•51 citations

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Xiao Yan Xu, Yang Qi, Long Zhang +3 more

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.

arXiv:1807.07574•Physical Review X•May 2, 2019•98 citations

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
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−\ensuremathϵ4\ensuremath{-}\ensuremath{\epsilon}4\ensuremath−\ensuremathϵ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.
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 $\ensuremath{\epsilon}=4\ensuremath{-}D$. 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.
Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+12+12+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (Nf{N}_{f}Nf​) and the strength of gauge fluctuations is mapped out. Here we focus on the large fermion flavor case (Nf=8{N}_{f}=8Nf​=8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu chiral O(2) universality whose properties are still largely unknown.
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 $\ensuremath{\epsilon}$ 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 $\ensuremath{\epsilon}$ 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.
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.
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.