Antiferromagnetic transitions of Dirac fermions in three dimensions

Huang, Yiqun; Guo, Huaiming; Maciejko, Joseph; Scalettar, Richard T.; Feng, Shiping

doi:10.1103/physrevb.102.155152

Antiferromagnetic transitions of Dirac fermions in three dimensions

Journal Article · Fri Oct 30 00:00:00 EDT 2020 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.102.155152· OSTI ID:1851968

^[1]; Guo, Huaiming ^[2]; ^[3]; Scalettar, Richard T. ^[4]; ^[5]

Beijing Normal University (China); OSTI
Beihang University, Beijing (China)
Univ. of Alberta, Edmonton, AB (Canada)
Univ. of California, Davis, CA (United States)
Beijing Normal University (China)

We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the π-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength U_c is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.

View Accepted Manuscript (DOE)

Research Organization:: University of California, Davis, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0014671

OSTI ID:: 1851968

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 15 Vol. 102; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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