We consider Lifshitz criticality (LC) with the dynamical critical exponent $z=2$ in one-dimensional interacting fermion systems with a filled Dirac sea. We report that interactions have crucial effects on Lifshitz criticality. Single-particle excitations are destabilized by an interaction and decay into the particle-hole continuum, which is reflected in the logarithmic divergence in the imaginary part of one-loop self-energy. We show that the system is sensitive to the sign of the interaction. The random-phase approximation shows that the collective particle-hole excitations emerge only when the interaction is repulsive. The dispersion of collective modes is gapless and linear. If the interaction is attractive, the one-loop renormalization group (RG) shows that there may exist a stable RG fixed point described by two coupling constants. We also show that the on-site interaction (without any other perturbations at the UV scale) would always turn on the relevant velocity perturbation to the quadratic Lagrangian in the RG flow, driving the system flow to the conformal-invariant criticality. In the numerical simulations of the lattice model at half filling, we find that, for either on-site positive or negative interactions, the dynamical critical exponent becomes $z=1$ in the infrared limit and the entanglement entropy is a logarithmic function of the system size $L$ . The work paves the way to study one-dimensional interacting LCs.We consider Lifshitz criticality (LC) with the dynamical critical exponent $z=2$ in one-dimensional interacting fermion systems with a filled Dirac sea. We report that interactions have crucial effects on Lifshitz criticality. Single-particle excitations are destabilized by an interaction and decay into the particle-hole continuum, which is reflected in the logarithmic divergence in the imaginary part of one-loop self-energy. We show that the system is sensitive to the sign of the interaction. The random-phase approximation shows that the collective particle-hole excitations emerge only when the interaction is repulsive. The dispersion of collective modes is gapless and linear. If the interaction is attractive, the one-loop renormalization group (RG) shows that there may exist a stable RG fixed point described by two coupling constants. We also show that the on-site interaction (without any other perturbations at the UV scale) would always turn on the relevant velocity perturbation to the quadratic Lagrangian in the RG flow, driving the system flow to the conformal-invariant criticality. In the numerical simulations of the lattice model at half filling, we find that, for either on-site positive or negative interactions, the dynamical critical exponent becomes $z=1$ in the infrared limit and the entanglement entropy is a logarithmic function of the system size $L$. The work paves the way to study one-dimensional interacting LCs.

arXiv:2302.13243Physical review. B./Physical review. BAug 16, 20232 citations

One-dimensional fermion pairing

Rafael Mendoza, MANUEL DE LLANO, Mauricio Fortes +1 more

Bulletin of the American Physical SocietyMar 11, 20080 citations

Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems

Veronika C. Stangier, Daniel E. Sheehy, Jörg Schmalian

We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the Sachdev-Ye-Kitaev (SYK)-inspired framework for Dirac systems introduced by Kim [Dirac fast scramblers, ], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the Sachdev-Ye-Kitaev (SYK)-inspired framework for Dirac systems introduced by Kim [Dirac fast scramblers, ], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.

arXiv:2509.25318Physical review. B./Physical review. BDec 15, 20253 citations

Critical properties of a one-dimensional interacting Fermi system in a magnetic field

V.I. Ponomarev

Physics Letters AApr 1, 19841 citation

We consider Lifshitz criticality (LC) with the dynamical critical exponent

z=2

in one-dimensional interacting fermion systems with a filled Dirac sea. We report that interactions have crucial effects on Lifshitz criticality. Single-particle excitations are destabilized by an interaction and decay into the particle-hole continuum, which is reflected in the logarithmic divergence in the imaginary part of one-loop self-energy. We show that the system is sensitive to the sign of the interaction. The random-phase approximation shows that the collective particle-hole excitations emerge only when the interaction is repulsive. The dispersion of collective modes is gapless and linear. If the interaction is attractive, the one-loop renormalization group (RG) shows that there may exist a stable RG fixed point described by two coupling constants. We also show that the on-site interaction (without any other perturbations at the UV scale) would always turn on the relevant velocity perturbation to the quadratic Lagrangian in the RG flow, driving the system flow to the conformal-invariant criticality. In the numerical simulations of the lattice model at half filling, we find that, for either on-site positive or negative interactions, the dynamical critical exponent becomes

z=1

in the infrared limit and the entanglement entropy is a logarithmic function of the system size

L

. The work paves the way to study one-dimensional interacting LCs.