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arXiv · 2001.09155

Soluble Fermionic Quantum Critical Point in Two Dimensions

Shouryya Ray·Matthias Vojta·Lukas Janssen
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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 $\eta_\phi = 2$, 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.

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Shouryya Ray, Matthias Vojta, Lukas Janssen. 2020-01-24. Soluble Fermionic Quantum Critical Point in Two Dimensions. https://doi.org/10.1103/physrevb.102.081112

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