Upper critical dimension for dirty Weyl semimetal-to-metal quantum phase transitions
Abstract
Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) ρ(E) ∼ |E|d−1 at energy E in d spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for d>2 and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in d=2 to $6$, here we show that d=2 and d=4 are the lower (dℓ) and upper (du) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for d ≥ 4 the associated correlation length exponent is found to be ν≈ 0.5 (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to z ≈ d/2 (numerically) for any d ≥ 3, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both dℓ and du.
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BibTeX
@misc{li2026upper,
title = {{Upper critical dimension for dirty Weyl semimetal-to-metal quantum phase transitions}},
author = {Yongtai Li and Bitan Roy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30265},
eprint = {2609.30265},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30265},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Upper critical dimension for dirty Weyl semimetal-to-metal quantum phase transitions
AU - Yongtai Li
AU - Bitan Roy
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30265
UR - https://arxiv.org/abs/2609.30265
AB - Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) ρ(E) ∼ |E|^d−1 at energy E in d spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for d>2 and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in d=2 to $6$, here we show that d=2 and d=4 are the lower (d_ℓ) and upper (d_u) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for d ≥ 4 the associated correlation length exponent is found to be ν≈ 0.5 (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to z ≈ d/2 (numerically) for any d ≥ 3, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both d_ℓ and d_u.
ER -