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:1801.03495 · Physical Review Letters

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials

Bitan Roy, Vladimir Juričić

Published Sep 24, 2018• 9 citations
arXivHTMLPDF

Abstract

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

DOI
10.1103/physrevlett.121.137601

Related papers

Collisionless transport close to a fermionic quantum critical point

Bitan Roy, Vladimir Juričić

We here report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar \omega \gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional massless Dirac fermions from a fully gapped insulator. Inside the critical regime gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC according to $\sigma^{\rm IB}_0 [1-N_b/(2N_f)]$ for $N_f \gg 1$ as $T \to 0$ to the leading order in $\epsilon$-expansion, where $N_f (N_b)$ is the fermionic(bosonic) flavor number, $\sigma^{\rm IB}_0$ is the OC of a non-interacting Dirac fluid, and $\epsilon=3-d$. Furthermore, the weight of the Drude peak inside the critical regime also gets suppressed following a universal scaling function, while maintaining its delta function profile. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalization of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented.

•Jan 10, 2018•2 citations

Itinerant quantum multicriticality of two-dimensional Dirac fermions

Bitan Roy, Pallab Goswami, Vladimir Juričić

We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $\text{O}({S}_{1})$ and $\text{O}({S}_{2})$ symmetries in the ordered phase. Performing a renormalization-group analysis by using the $\ensuremath{\epsilon}=(3\ensuremath{-}d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged $\text{O}({S}_{1}+{S}_{2})$ chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $\text{O}({S}_{1})$ or $\text{O}({S}_{2})$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.

arXiv:1712.05400•Physical review. B./Physical review. B•May 11, 2018•22 citations

Quantum Criticality between Topological and Band Insulators in 3+1 Dimensions

Pallab Goswami, Sudip Chakravarty

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.

arXiv:1101.2210•Physical Review Letters•Nov 2, 2011•233 citations

Universal electrical transport of composite Fermi liquid to Metal transition in Moiré systems

Youxuan Wang, R. Liu, Feng Liu +1 more

We compute universal electrical transport near continuous transitions between a composite Fermi liquid (CFL) and a metallic phase in moire Chern bands, focusing on fillings $ν=-1/2$ and $ν=-3/4$. The critical theory represents a novel QED-Chern-Simons framework: a charged sector at a bosonic Laughlin-superfluid critical point is coupled, via emergent gauge fields and Chern-Simons mixing, to a neutral spinon Fermi surface. Integrating out matter fields to quadratic order yields an explicit Ioffe-Larkin composition rule for the full resistivity tensor, showing how longitudinal channels add in series while Chern-Simons terms generate Hall response. To obtain the DC limit in the quantum critical fan, we develop a controlled large-N expansion where both fermion flavors and Chern-Simons levels scale with $N$, and solve a quantum Boltzmann equation at leading nontrivial order $1/N$. Gauge-mediated inelastic scattering removes the collisionless Drude singularity and produces a universal scaling function $Σ(ω/T)$ and finite DC conductivities $σ(0) \approx 0.033 e^2/\hbar$ ($ν=-1/2$) and $0.047 e^2/\hbar$ ($ν=-3/4$). We also identify a Chern-Simons "filtering" mechanism that suppresses transmission of Landau damping from the spinon Fermi surface to the critical gauge mode. Our approach provides concrete transport diagnostics for detecting quantum criticality in moire superlattices.

arXiv:2602.15334•Feb 17, 2026•0 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

Driven Critical Dynamics in Strongly Interacting Dirac Systems

Zhi Zeng, Yin-Kai Yu, Zhixuan Li +2 more

The conventional Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. In this paper, by leveraging the large-scale quantum Monte Carlo simulation, we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point (QCP) triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. A remarkable discovery is that, despite the existence of the gapless initial phase, the driven dynamics can still be captured by the FTS form. This leads us to propose a generalized criterion for the validity of KZM and FTS with a gapless initial state. Accordingly, our results significantly generalize the KZM theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Through successfully extending the KZM and FTS theory to the strongly interacting Dirac QCP, our work not only brings new fundamental perspective into the nonequilibrium critical dynamics, but also provides a novel theoretical approach to fathom quantum critical properties in fermionic systems.

arXiv:2403.19258•Mar 28, 2024•1 citation
Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.
We here report the scaling of optical conductivity (OC) in the \emph{collisionless} regime (ℏω≫kBT\hbar \omega \gg k_B Tℏω≫kB​T) in the vicinity of a relativistic quantum critical point, separating two-dimensional massless Dirac fermions from a fully gapped insulator. Inside the critical regime gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC according to σ0IB[1−Nb/(2Nf)]\sigma^{\rm IB}_0 [1-N_b/(2N_f)]σ0IB​[1−Nb​/(2Nf​)] for Nf≫1N_f \gg 1Nf​≫1 as T→0T \to 0T→0 to the leading order in ϵ\epsilonϵ-expansion, where Nf(Nb)N_f (N_b)Nf​(Nb​) is the fermionic(bosonic) flavor number, σ0IB\sigma^{\rm IB}_0σ0IB​ is the OC of a non-interacting Dirac fluid, and ϵ=3−d\epsilon=3-dϵ=3−d. Furthermore, the weight of the Drude peak inside the critical regime also gets suppressed following a universal scaling function, while maintaining its delta function profile. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalization of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented.
We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d=2d=2d=2) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1)\text{O}({S}_{1})O(S1​) and O(S2)\text{O}({S}_{2})O(S2​) symmetries in the ordered phase. Performing a renormalization-group analysis by using the $\ensuremath{\epsilon}=(3\ensuremath{-}d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2)\text{O}({S}_{1}+{S}_{2})O(S1​+S2​) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1)\text{O}({S}_{1})O(S1​) or O(S2)\text{O}({S}_{2})O(S2​) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.
Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.
We compute universal electrical transport near continuous transitions between a composite Fermi liquid (CFL) and a metallic phase in moire Chern bands, focusing on fillings ν=−1/2ν=-1/2ν=−1/2 and ν=−3/4ν=-3/4ν=−3/4. The critical theory represents a novel QED-Chern-Simons framework: a charged sector at a bosonic Laughlin-superfluid critical point is coupled, via emergent gauge fields and Chern-Simons mixing, to a neutral spinon Fermi surface. Integrating out matter fields to quadratic order yields an explicit Ioffe-Larkin composition rule for the full resistivity tensor, showing how longitudinal channels add in series while Chern-Simons terms generate Hall response. To obtain the DC limit in the quantum critical fan, we develop a controlled large-N expansion where both fermion flavors and Chern-Simons levels scale with NNN, and solve a quantum Boltzmann equation at leading nontrivial order 1/N1/N1/N. Gauge-mediated inelastic scattering removes the collisionless Drude singularity and produces a universal scaling function Σ(ω/T)Σ(ω/T)Σ(ω/T) and finite DC conductivities σ(0)≈0.033e2/ℏσ(0) \approx 0.033 e^2/\hbarσ(0)≈0.033e2/ℏ (ν=−1/2ν=-1/2ν=−1/2) and 0.047e2/ℏ0.047 e^2/\hbar0.047e2/ℏ (ν=−3/4ν=-3/4ν=−3/4). We also identify a Chern-Simons "filtering" mechanism that suppresses transmission of Landau damping from the spinon Fermi surface to the critical gauge mode. Our approach provides concrete transport diagnostics for detecting quantum criticality in moire superlattices.
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.
The conventional Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. In this paper, by leveraging the large-scale quantum Monte Carlo simulation, we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point (QCP) triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. A remarkable discovery is that, despite the existence of the gapless initial phase, the driven dynamics can still be captured by the FTS form. This leads us to propose a generalized criterion for the validity of KZM and FTS with a gapless initial state. Accordingly, our results significantly generalize the KZM theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Through successfully extending the KZM and FTS theory to the strongly interacting Dirac QCP, our work not only brings new fundamental perspective into the nonequilibrium critical dynamics, but also provides a novel theoretical approach to fathom quantum critical properties in fermionic systems.