Soluble Fermionic Quantum Critical Point in Two Dimensions

Abstract

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 ${\eta }_{\varphi }=2$, 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.

arXiv comment6+8 pages, 4+3 figures. (v2) Discussion of results expanded, typos corrected, some technical details shifted to Supplemental Material; final version as published (PRB Rapid Comm.)

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Cited by in corpus (7)

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