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:2204.05319 · Physical review. B./Physical review. B

Quantum-critical electrodynamics of Luttinger fermions

Santanu Dey, Joseph Maciejko

Published Jul 20, 2022• 3 citations
arXivHTMLPDF

Abstract

We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative U(1) quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations and can thus also be viewed as a U(1) spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.

DOI
10.1103/physrevb.106.035140

Related papers

Spin-liquid Mott quantum criticality in two dimensions: Destabilization of a spinon Fermi surface and emergence of one-dimensional spin dynamics

Jae-Ho Han, Yong-Heum Cho, Ki‐Seok Kim

Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted $XY$ universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2{k}_{F}$ transfer momentum, where ${k}_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.

arXiv:1606.07544•Physical review. B./Physical review. B•Jun 16, 2017•1 citation

Quantum Electrodynamics in 2+1 Dimensions, Confinement, and the Stability of U(1) Spin Liquids

Flavio S. Nogueira, Hagen M. Kleinert

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.

arXiv:cond-mat/0501022•Physical Review Letters•Oct 20, 2005•34 citations

Superconducting quantum criticality in three-dimensional Luttinger semimetals

Igor Boettcher, Igor F. Herbut

We study a simple model of three-dimensional fermions close to a quadratic band touching point, built from the celebrated Luttinger single-particle Hamiltonian and an attractive contact interaction between the particles. Such a system displays a quantum critical point between the semimetallic and an $s$-wave superconducting phase at which the low-energy ``Luttinger fermions'' are inextricably coupled to the order parameter fluctuations. The quantum critical point is perturbatively accessible near four spatial dimensions, where it features nontrivial scaling with dynamical exponent $1<z<2$ and emergent rotational and particle-hole symmetries. Some features of the criticality, such as oscillatory corrections to scaling and its enhanced symmetry, are discussed.

arXiv:1603.00031•Physical review. B./Physical review. B•May 23, 2016•82 citations

Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis

Santanu Pal, Anirban Mukherjee, Siddhartha Lal

We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan–Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel–Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU (2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al . We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.

arXiv:1811.05222•New Journal of Physics•Feb 11, 2019•15 citations

Effective Field Theories for Metallic Quantum Critical Points

Shouvik Sur

In this thesis we study the scaling properties of unconventional metals that arise at quantum critical points using low-energy effective field theories. Due to high rate of scatterings between electrons and critical fluctuations of the order parameter associated with spontaneous symmetry breaking, Landau’s Fermi liquid theory breaks down at the critical points. The theories that describe these critical points generally flow into strong coupling regimes at low energy in two space dimensions. Here we develop and utilize renormalization group methods that are suitable for the interacting non-Fermi liquids. We focus on the critical points arising at excitonic, and commensurate spin and charge density wave transitions. By controlled analyses we find stable non-Fermi liquid and marginal Fermi liquid states, and extract the scaling behaviour. The field theories for the non-Fermi liquids are characterized by symmetry groups, local curvature of the Fermi surface, the dispersion of the order parameter fluctuations, and dimensions of space and Fermi surface.

•Oct 15, 2015•0 citations

Emergent Gauge Flux in Mixed QED 3 with Flavor Chemical Potential: Implications for Magnetized U(1) Dirac Spin Liquids

Chuang Chen, Urban F. P. Seifert, Kexin Feng +3 more

We design a lattice model of a “mixed” U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations. In this mixed construction, dynamical magnetic monopole events are suppressed in the temporal-continuum limit. For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics ( QED 3 ) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, which corresponds to a Zeeman field perturbing the Dirac spin liquid, we find a “chiral flux” phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. We use field-theory arguments to argue that in this state a U ( 1 ) m magnetic symmetry is spontaneously broken, leading to a gapless photon mode. Because of spin-flux attachment this mode would contribute to the low-energy longitudinal spin response. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

arXiv:2508.08528•Physical Review X•Sep 28, 2026•1 citation
We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative U(1) quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations and can thus also be viewed as a U(1) spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.
Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XYXYXY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a 2kF2{k}_{F}2kF​ transfer momentum, where kF{k}_{F}kF​ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.
Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.
We study a simple model of three-dimensional fermions close to a quadratic band touching point, built from the celebrated Luttinger single-particle Hamiltonian and an attractive contact interaction between the particles. Such a system displays a quantum critical point between the semimetallic and an sss-wave superconducting phase at which the low-energy ``Luttinger fermions'' are inextricably coupled to the order parameter fluctuations. The quantum critical point is perturbatively accessible near four spatial dimensions, where it features nontrivial scaling with dynamical exponent 1<z<21<z<21<z<2 and emergent rotational and particle-hole symmetries. Some features of the criticality, such as oscillatory corrections to scaling and its enhanced symmetry, are discussed.
We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan–Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel–Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU (2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al . We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.
In this thesis we study the scaling properties of unconventional metals that arise at quantum critical points using low-energy effective field theories. Due to high rate of scatterings between electrons and critical fluctuations of the order parameter associated with spontaneous symmetry breaking, Landau’s Fermi liquid theory breaks down at the critical points. The theories that describe these critical points generally flow into strong coupling regimes at low energy in two space dimensions. Here we develop and utilize renormalization group methods that are suitable for the interacting non-Fermi liquids. We focus on the critical points arising at excitonic, and commensurate spin and charge density wave transitions. By controlled analyses we find stable non-Fermi liquid and marginal Fermi liquid states, and extract the scaling behaviour. The field theories for the non-Fermi liquids are characterized by symmetry groups, local curvature of the Fermi surface, the dispersion of the order parameter fluctuations, and dimensions of space and Fermi surface.
We design a lattice model of a “mixed” U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations. In this mixed construction, dynamical magnetic monopole events are suppressed in the temporal-continuum limit. For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics ( QED 3 ) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, which corresponds to a Zeeman field perturbing the Dirac spin liquid, we find a “chiral flux” phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. We use field-theory arguments to argue that in this state a U ( 1 ) m magnetic symmetry is spontaneously broken, leading to a gapless photon mode. Because of spin-flux attachment this mode would contribute to the low-energy longitudinal spin response. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.