TY - JOUR
T1 - Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
AU - Lunts, Peter
AU - Albergo, Michael S.
N1 - Funding Information:
We are extremely indebted to Bob Carpenter for teaching us the auto-tuning procedure used in industry applications of HMC and employed in this paper. We thank Phiala Shanahan for insightful discussions. P.L. thanks Subir Sachdev, the attendees of the Aspen Center for Physics conference ‘New Directions in Strong Correlation Physics: From Strange Metals to Topological Superconductivity,’ and in particular Sung-Sik Lee for useful discussions. We thank Sung-Sik Lee for comments on the manuscript. We thank Nick Carriero and the other members of the Scientific Computing Core at Flatiron Institute for their assistance in running the codes. M.A. and M.L. are grateful for the hospitality of the Center for Computational Quantum Physics at the Flatiron Institute. The Flatiron Institute is a division of the Simons Foundation. This work was partially completed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. P.L. is supported by the Simons Foundation. M.A. is supported by the National Science Foundation under the award PHY-2141336. M.L. is supported by the National Science Foundation under Award No. 1903031.
Funding Information:
We are extremely indebted to Bob Carpenter for teaching us the auto-tuning procedure used in industry applications of HMC and employed in this paper. We thank Phiala Shanahan for insightful discussions. P.L. thanks Subir Sachdev, the attendees of the Aspen Center for Physics conference ‘New Directions in Strong Correlation Physics: From Strange Metals to Topological Superconductivity,’ and in particular Sung-Sik Lee for useful discussions. We thank Sung-Sik Lee for comments on the manuscript. We thank Nick Carriero and the other members of the Scientific Computing Core at Flatiron Institute for their assistance in running the codes. M.A. and M.L. are grateful for the hospitality of the Center for Computational Quantum Physics at the Flatiron Institute. The Flatiron Institute is a division of the Simons Foundation. This work was partially completed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. P.L. is supported by the Simons Foundation. M.A. is supported by the National Science Foundation under the award PHY-2141336. M.L. is supported by the National Science Foundation under Award No. 1903031.
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/12
Y1 - 2023/12
N2 - A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid behavior and superconducting phase. A minimal model for this transition is the O(3) spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the O(3) spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of 80 × 80 sites. We find a strong violation of the Hertz-Millis form, contrary to all previous numerical results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect “hot-spot’" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.
AB - A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid behavior and superconducting phase. A minimal model for this transition is the O(3) spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the O(3) spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of 80 × 80 sites. We find a strong violation of the Hertz-Millis form, contrary to all previous numerical results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect “hot-spot’" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.
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U2 - 10.1038/s41467-023-37686-4
DO - 10.1038/s41467-023-37686-4
M3 - Article
C2 - 37137882
AN - SCOPUS:85157978131
SN - 2041-1723
VL - 14
JO - Nature communications
JF - Nature communications
IS - 1
M1 - 2547
ER -