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PreprintCC BY 4.0arXiv

Quantum Critical Solids

  • Subham Dutta Chowdhury
  • Leo Radzihovsky
  • Luca V. Delacrétaz
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Abstract

We study the fate of quantum solids with a vanishing velocity of transverse phonons. Such ``floppy'' solids exhibit a cubic elastic nonlinearity that is relevant in spatial dimensions d<4 and drives the system to a strongly-coupled Lifshitz quantum critical point in d=3, that we analyze in an ε= 4−d expansion. The associated phase transition is generically first-order, preempting the system's full access to the strongly-coupled fixed point. Nevertheless, the critical data of this quantum critical point is accessible within a Ginzburg region in the vicinity of the transition. This cubic nonlinearity vanishes exactly in d=2, where the leading interactions are instead quartic and are marginal, leading to weak logarithmic singularities. We discuss possible realizations of this ``crystal Lifshitz criticality'' in quantum materials.

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Cite

BibTeXRIS
BibTeX
@misc{chowdhury2026quantum,
  title = {{Quantum Critical Solids}},
  author = {Subham Dutta Chowdhury and Leo Radzihovsky and Luca V. Delacrétaz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16147},
  eprint = {2609.16147},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16147},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum Critical Solids
AU  - Subham Dutta Chowdhury
AU  - Leo Radzihovsky
AU  - Luca V. Delacrétaz
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16147
UR  - https://arxiv.org/abs/2609.16147
AB  - We study the fate of quantum solids with a vanishing velocity of transverse phonons. Such ``floppy'' solids exhibit a cubic elastic nonlinearity that is relevant in spatial dimensions d<4 and drives the system to a strongly-coupled Lifshitz quantum critical point in d=3, that we analyze in an ε= 4−d expansion. The associated phase transition is generically first-order, preempting the system's full access to the strongly-coupled fixed point. Nevertheless, the critical data of this quantum critical point is accessible within a Ginzburg region in the vicinity of the transition. This cubic nonlinearity vanishes exactly in d=2, where the leading interactions are instead quartic and are marginal, leading to weak logarithmic singularities. We discuss possible realizations of this ``crystal Lifshitz criticality'' in quantum materials.
ER  -