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arXiv:1712.05400 · Physical review. B./Physical review. B

Itinerant quantum multicriticality of two-dimensional Dirac fermions

Bitan Roy, Pallab Goswami, Vladimir Juričić

Published May 11, 2018• 22 citations
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Abstract

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.

DOI
10.1103/physrevb.97.205117

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The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, we study the fermionic quantum criticality with enlarged Ising×\times×Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine the critical range in which the quantum fluctuations may render the phase transition continuous. We find that the Ising criticality is continuous only when the flavor numbers of four-component Dirac fermions Nf≥1/4N_f\geq1/4Nf​≥1/4. Using the εεε expansion in four space-time dimensions, we then study the Ising×\times×Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising×\times×Ising Gross-Neveu-Yukawa universality class. Further, the correlation scaling behavior for the fermion bilinear on the honeycomb lattice at the multicritical point are also briefly discussed.
We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with O(N1)\mathrm{O}({N}_{1})O(N1​) and O(N2)\mathrm{O}({N}_{2})O(N2​) symmetries, respectively. Using $\ensuremath{\epsilon}$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent O(N1+N2)\mathrm{O}({N}_{1}+{N}_{2})O(N1​+N2​) symmetry for arbitrary values of N1{N}_{1}N1​ and N2{N}_{2}N2​ and fermion flavor numbers Nf{N}_{\mathrm{f}}Nf​ as long as the corresponding representation of the Clifford algebra exists. Small O(N)\mathrm{O}(N)O(N)-breaking perturbations near the chiral O(N)\mathrm{O}(N)O(N) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic O(N)\mathrm{O}(N)O(N) fixed point, which is stable only when N<3N<3N<3. As a by-product, we obtain predictions for the critical behavior of the chiral O(N)\mathrm{O}(N)O(N) universality classes for arbitrary NNN and fermion flavor number Nf{N}_{\mathrm{f}}Nf​. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.