Fermi-Point Topology Determines Emergent Conformal Criticality in Extended Quantum Spin Chains
Abstract
Quantum criticality in one-dimensional quantum systems is characterized by emergent conformal field theories (CFTs), whose central charge counts independent gapless degrees of freedom. Establishing a microscopic connection between this universal conformal structure and the momentum-space topology of the underlying quasiparticle spectrum remains challenging. Here, we uncover a direct correspondence between Fermi-point topology, conformal criticality, and quantum entanglement in an extended quantum spin chain with competing cluster interactions, exchange anisotropy, and a transverse magnetic field. We show that interaction- and field-driven Lifshitz transitions generate conformal critical phases with effective central charges ceff=1/2, $1$, 3/2, $2$, and $3$, including a multicritical point where Ising and Luttinger-liquid sectors coexist. Importantly, the central charge is not determined simply by the number of lattice gap closings or Fermi points, but by the number and conformal content of independent low-energy continuum sectors after accounting for lattice symmetries, reciprocal-lattice identifications, and mode equivalences. Thus, Lifshitz transitions may leave the conformal anomaly unchanged or modify the central charge depending on whether spectral reconstruction generates new independent continuum sectors. Real- and momentum-space entanglement spectra provide complementary microscopic signatures, revealing both the conformal content and momentum-space organization of critical modes. Our results establish a microscopic framework linking Fermi-point topology to emergent CFTs and show how interaction-driven spectral reconstruction can generate higher-central-charge criticality and unconventional multicritical behavior.
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BibTeX
@misc{abbasi2026fermipoint,
title = {{Fermi-Point Topology Determines Emergent Conformal Criticality in Extended Quantum Spin Chains}},
author = {Mohammad Abbasi and Saeed Mahdavifar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03708},
eprint = {2609.03708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03708},
}
RIS
TY - UNPB
TI - Fermi-Point Topology Determines Emergent Conformal Criticality in Extended Quantum Spin Chains
AU - Mohammad Abbasi
AU - Saeed Mahdavifar
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03708
UR - https://arxiv.org/abs/2609.03708
AB - Quantum criticality in one-dimensional quantum systems is characterized by emergent conformal field theories (CFTs), whose central charge counts independent gapless degrees of freedom. Establishing a microscopic connection between this universal conformal structure and the momentum-space topology of the underlying quasiparticle spectrum remains challenging. Here, we uncover a direct correspondence between Fermi-point topology, conformal criticality, and quantum entanglement in an extended quantum spin chain with competing cluster interactions, exchange anisotropy, and a transverse magnetic field. We show that interaction- and field-driven Lifshitz transitions generate conformal critical phases with effective central charges c_eff=1/2, $1$, 3/2, $2$, and $3$, including a multicritical point where Ising and Luttinger-liquid sectors coexist. Importantly, the central charge is not determined simply by the number of lattice gap closings or Fermi points, but by the number and conformal content of independent low-energy continuum sectors after accounting for lattice symmetries, reciprocal-lattice identifications, and mode equivalences. Thus, Lifshitz transitions may leave the conformal anomaly unchanged or modify the central charge depending on whether spectral reconstruction generates new independent continuum sectors. Real- and momentum-space entanglement spectra provide complementary microscopic signatures, revealing both the conformal content and momentum-space organization of critical modes. Our results establish a microscopic framework linking Fermi-point topology to emergent CFTs and show how interaction-driven spectral reconstruction can generate higher-central-charge criticality and unconventional multicritical behavior.
ER -