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.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:2602.15334Feb 17, 20260 citations

Kondo signatures in Dirac spin liquids: Non-Abelian bosonization after Chern-Simons fermionization

Rui Wang, Wang, Yilin, Y. X. Zhao +1 more

Quantum impurities serve as in-situ probes of the frustrated quantum magnets, and Dirac spin liquids are an important class of quantum spin liquids. Here, we present a general method, a combination of the Chern-Simons fermionization and the Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spin liquids. Under the Chern-Simons fermionization, the gauge fluctuations are apparently suppressed and the low-energy physics is described by a number of Dirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)D effective theory can be further reduced into the (1+1)D Wess-Zumino-Witten theory by rotational symmetry, where the pseudospin-exchange between Dirac fermions and the impurity can then be solved by the non-Abelian bosonization. Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified, respectively, depending on the relevance of the impurity scattering among the Dirac valleys. This leads to experimental fingerprints for Dirac spin liquids, including a Kondo-induced magneto-thermal effect, a non-monotonous thermal conductivity during the crossover, and an anisotropic spin correlation function.Quantum impurities serve as in-situ probes of the frustrated quantum magnets, and Dirac spin liquids are an important class of quantum spin liquids. Here, we present a general method, a combination of the Chern-Simons fermionization and the Wess-Zumino-Witten theory, to study the quantum impurity in Dirac spin liquids. Under the Chern-Simons fermionization, the gauge fluctuations are apparently suppressed and the low-energy physics is described by a number of Dirac valleys with valley-dependent pseudospin-momentum locking. The (2+1)D effective theory can be further reduced into the (1+1)D Wess-Zumino-Witten theory by rotational symmetry, where the pseudospin-exchange between Dirac fermions and the impurity can then be solved by the non-Abelian bosonization. Consequently, fixed points of Fermi liquid and non-Fermi liquid are identified, respectively, depending on the relevance of the impurity scattering among the Dirac valleys. This leads to experimental fingerprints for Dirac spin liquids, including a Kondo-induced magneto-thermal effect, a non-monotonous thermal conductivity during the crossover, and an anisotropic spin correlation function.

arXiv:2010.05022Oct 10, 20200 citations

Beyond Landau's theory of Fermi liquids

Hagen M. Kleinert

Physics Letters AJul 1, 19814 citations

Theory of competing Chern-Simons orders and emergent phase transitions

Rui Wang, Z. Y. Xie, Baigeng Wang +1 more

Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a systematic framework to investigate the competition between emergent phases in frustrated two-dimensional XY quantum magnets. Application of the method to the antiferromagnetic honeycomb spin-1/2 $J_1$ - $J_2$ XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid that was proposed earlier in the literature. Namely, the Chern-Simons superconductor describes the planar Néel state, while the Chern-Simons exciton insulator corresponds to the non-uniform chiral spin-liquid. These results are further confirmed by our high-precision tensor network calculation, which provides the first numerical evidence for the transition from Néel order to a non-uniform chiral spin-liquid. We argue that the developed method can be applied to other frustrated quantum magnets of XXZ type and can detect unconventional phase transitions.Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a systematic framework to investigate the competition between emergent phases in frustrated two-dimensional XY quantum magnets. Application of the method to the antiferromagnetic honeycomb spin-1/2 $J_1$-$J_2$ XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid that was proposed earlier in the literature. Namely, the Chern-Simons superconductor describes the planar Néel state, while the Chern-Simons exciton insulator corresponds to the non-uniform chiral spin-liquid. These results are further confirmed by our high-precision tensor network calculation, which provides the first numerical evidence for the transition from Néel order to a non-uniform chiral spin-liquid. We argue that the developed method can be applied to other frustrated quantum magnets of XXZ type and can detect unconventional phase transitions.

arXiv:2101.04864Jan 13, 20210 citations

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.

J_1

J_2

XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid that was proposed earlier in the literature. Namely, the Chern-Simons superconductor describes the planar Néel state, while the Chern-Simons exciton insulator corresponds to the non-uniform chiral spin-liquid. These results are further confirmed by our high-precision tensor network calculation, which provides the first numerical evidence for the transition from Néel order to a non-uniform chiral spin-liquid. We argue that the developed method can be applied to other frustrated quantum magnets of XXZ type and can detect unconventional phase transitions.