Gross-Neveu-Heisenberg criticality from $2+\boldsymbol{\epsilon}$ expansion
Phys. Rev. B 107, 035151 (2023) The Gross-Neveu-Heisenberg universality class describes a continuous quantum phase transition between a Dirac semimetal and an antiferromagnetic insulator. Such quantum critical points have originally been discussed in the context of Hubbard models on $\pi$-flux and h...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
06.09.2022
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Subjects | |
Online Access | Get full text |
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Summary: | Phys. Rev. B 107, 035151 (2023) The Gross-Neveu-Heisenberg universality class describes a continuous quantum
phase transition between a Dirac semimetal and an antiferromagnetic insulator.
Such quantum critical points have originally been discussed in the context of
Hubbard models on $\pi$-flux and honeycomb lattices, but more recently also in
Bernal-stacked bilayer models, of potential relevance for bilayer graphene.
Here, we demonstrate how the critical behavior of this fermionic universality
class can be computed within an $\epsilon$ expansion around the lower critical
space-time dimension of two. This approach is complementary to the previously
studied expansion around the upper critical dimension of four. The crucial
technical novelty near the lower critical dimension is the presence of
different four-fermion interaction channels at the critical point, which we
take into account in a Fierz-complete way. By interpolating between the lower
and upper critical dimensions, we obtain improved estimates for the critical
exponents in 2+1 space-time dimensions. For the situation relevant to
single-layer graphene, we find an unusually small leading-correction-to-scaling
exponent, arising from the competition between different interaction channels.
This suggests that corrections to scaling may need to be taken into account
when comparing analytical estimates with numerical data from finite-size
extrapolations. |
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DOI: | 10.48550/arxiv.2209.02734 |