• DOI:10.1103/PHYSREVB.102.081112
• Corpus ID: 210920176

Soluble fermionic quantum critical point in two dimensions

@article{Ray2020SolubleFQ,
  title={Soluble fermionic quantum critical point in two dimensions},
  author={Shouryya Ray and Matthias Vojta and Lukas Janssen},
  journal={Physical Review B},
  year={2020},
  volume={102}
}

• Shouryya Ray, M. Vojta, L. Janssen
• Published 24 January 2020
• Physics
• Physical Review B

We study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical behavior can be computed exactly, and we explicitly derive the scaling laws of various observables. While the order-parameter correlation function at criticality satisfies the usual power law with anomalous exponent $\eta_\phi = 2$, the correlation length and the expectation value of the order parameter exhibit essential singularities upon approaching the quantum critical point from the insulating side, akin to the Berezinskii-Kosterlitz-Thouless transition. The susceptibility, on the other hand, has a power-law divergence with non-mean-field exponent $\gamma = 2$. On the semimetallic side, the correlation length remains infinite, leading to an emergent scale invariance throughout this phase.