Abstract
We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions the direct DSM-BI transition can either $(i)$ become a first-order transition, or $(ii)$ get avoided by an intervening broken-symmetry phase (BSP). We perform a renormalization group analysis by perturbing away from the one-dimensional limit with the small parameter $\epsilon = 1/n$, augmented with a $1/n$ expansion (parametrically suppressing quantum fluctuations in higher dimension). We identify charge density wave (CDW), antiferromagnet (AFM) and singlet s-wave superconductor as the three dominant candidates for the BSP. The onset of any such order at strong coupling $(\sim \epsilon)$ takes place through a continuous quantum phase transition across multicritical point. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2)-symmetric quantum critical points separating the ASM from the AFM and superconducting orders, respectively. Our results can be germane for a uniaxially strained honeycomb lattice or organic compound $\alpha$-(BEDT-TTF)$_2\text{I}_3$.
Highlights
A Dirac semimetal stands as a paradigmatic representative of a symmetry-protected gapless topological phase of matter that, for example, in two spatial dimensions, can be realized in pristine monolayer graphene [1,2,3]
We show that the anisotropic semimetal (ASM) can undergo a continuous quantum phase transition at strong interaction coupling through a multicritical point and enter into various broken-symmetry phases
For a spinless ASM obtained from a microscopic strained honeycomb lattice model that is free of frustration, the charge density wave (CDW) order is expected to preempt the topological first-order transition between the Dirac semimetal and band insulator, since the CDW order completely gaps out critical excitations, producing a uniform mass gap in the spectrum
Summary
A Dirac semimetal stands as a paradigmatic representative of a symmetry-protected gapless topological phase of matter that, for example, in two spatial dimensions, can be realized in pristine monolayer graphene [1,2,3]. We consider an alternative scenario that could occur at strong coupling, wherein the Dirac semimetal can be separated from the band insulator by a fluctuation-driven first-order transition. In addition to CDW, AFM, and s-wave pairing, a Dirac semimetal can accommodate additional fully gapped orders, such as a quantum anomalous/spin-Hall insulator or Kekule valence-bond solid [8].
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