Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2007.15175 · Physical review. B./Physical review. B

Antiferromagnetic transitions of Dirac fermions in three dimensions

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

Published Oct 30, 2020• 13 citations
arXivHTMLPDF

Abstract

We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $\ensuremath{\pi}$-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.

DOI
10.1103/physrevb.102.155152

Related papers

Quantum phase transitions of multispecies Dirac fermions

Huaiming Guo, Lei Wang, Richard T. Scalettar

We use the determinant quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\ensuremath{\pi}$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength ${U}_{c}$ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the bandwidth. Although ${U}_{c}$ is monotonic, at fixed inverse temperature $\ensuremath{\beta}$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be nonmonotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.

arXiv:1710.03365•Physical review. B./Physical review. B•Jun 28, 2018•16 citations

Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models

Francesco Parisen Toldin, Martin Hohenadler, Fakher F. Assaad +1 more

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\pi$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

•Nov 10, 2014•0 citations

Fermionic quantum criticality in honeycomb and π -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

Francesco Parisen Toldin, Martin Hohenadler, Fakher F. Assaad +1 more

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\ensuremath{\pi}$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

arXiv:1411.2502•Physical Review B•Apr 6, 2015•197 citations

Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model

Eduardo Ibarra-García-Padilla, Rick Mukherjee, Randall G. Hulet +3 more

The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, ${t}_{\ensuremath{\perp}}$, is unequal to the intraplane tunneling $t$. This model interpolates between the three-dimensional isotropic (${t}_{\ensuremath{\perp}}=t$) and two-dimensional (2D; ${t}_{\ensuremath{\perp}}=0$) systems. We show that at fixed interaction strength to tunneling ratio ($U/t$), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the N\'eel temperature ${T}_{\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}}$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal $U/t$. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.

arXiv:2006.02029•Physical Review A•Sep 29, 2020•23 citations

Observation of the antiferromagnetic phase transition in the fermionic Hubbard model

Hou-Ji Shao, Yu‐Xuan Wang, Dezhi Zhu +9 more

The fermionic Hubbard model (FHM)[1], despite its simple form, captures essential features of strongly correlated electron physics. Ultracold fermions in optical lattices[2, 3] provide a clean and well-controlled platform for simulating FHM. Doping its antiferromagnetic ground state at half filling, various exotic phases are expected to arise in the FHM simulator, including stripe order[4], pseudogap[5], and d-wave superconductors[6], offering valuable insights into high-temperature superconductivity[7{9]. Although notable progress, such as the observation of antiferromagnetic correlations over short[10] and extended distances[11], has been obtained, the antiferromagnetic phase has yet to be realized due to the significant challenges of achieving low temperatures in a large and uniform quantum simulator. Here, we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature, and doping concentration are finely tuned to approach their respective critical values, sharp increases in the spin structure factor (SSF) are observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class[12]. At half filling and with optimal interaction strength, the measured SSF reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results set the stage for exploring the low-temperature phase diagram of FHM.

arXiv:2402.14605•Feb 22, 2024•1 citation

Quantum Monte Carlo Simulation of the Chiral Heisenberg Gross-Neveu-Yukawa Phase Transition with a Single Dirac Cone

Thomas C. Lang, Andreas Martin Läuchli

We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with N=4 Dirac spinor components subject to a repulsive, local four fermion interaction in (2+1)D. Here we employ a two-dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and π-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of U_{c}=6.76(1) as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition, we extract a self-consistent set of critical exponents ν=0.98(1), η_{ϕ}=0.53(1), η_{ψ}=0.18(1), and β=0.75(1). We provide evidence for the continuous degradation of the quasiparticle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally, we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction U, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.

arXiv:1808.01230•Physical Review Letters•Sep 25, 2019•73 citations
We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the \ensuremathπ\ensuremath{\pi}\ensuremathπ-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 Uc{U}_{c}Uc​ 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.
We use the determinant quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\ensuremath{\pi}$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the bandwidth. Although Uc{U}_{c}Uc​ is monotonic, at fixed inverse temperature $\ensuremath{\beta}$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be nonmonotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.
Fermionic quantum criticality in honeycomb and π\piπ-flux Hubbard models
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π\piπ-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\ensuremath{\pi}$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.
The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, ${t}_{\ensuremath{\perp}}$, is unequal to the intraplane tunneling ttt. This model interpolates between the three-dimensional isotropic (${t}_{\ensuremath{\perp}}=t$) and two-dimensional (2D; ${t}_{\ensuremath{\perp}}=0$) systems. We show that at fixed interaction strength to tunneling ratio (U/tU/tU/t), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the N\'eel temperature ${T}_{\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}}$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal U/tU/tU/t. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.
The fermionic Hubbard model (FHM)[1], despite its simple form, captures essential features of strongly correlated electron physics. Ultracold fermions in optical lattices[2, 3] provide a clean and well-controlled platform for simulating FHM. Doping its antiferromagnetic ground state at half filling, various exotic phases are expected to arise in the FHM simulator, including stripe order[4], pseudogap[5], and d-wave superconductors[6], offering valuable insights into high-temperature superconductivity[7{9]. Although notable progress, such as the observation of antiferromagnetic correlations over short[10] and extended distances[11], has been obtained, the antiferromagnetic phase has yet to be realized due to the significant challenges of achieving low temperatures in a large and uniform quantum simulator. Here, we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature, and doping concentration are finely tuned to approach their respective critical values, sharp increases in the spin structure factor (SSF) are observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class[12]. At half filling and with optimal interaction strength, the measured SSF reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results set the stage for exploring the low-temperature phase diagram of FHM.
We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with N=4 Dirac spinor components subject to a repulsive, local four fermion interaction in (2+1)D. Here we employ a two-dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and π-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of U_{c}=6.76(1) as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition, we extract a self-consistent set of critical exponents ν=0.98(1), η_{ϕ}=0.53(1), η_{ψ}=0.18(1), and β=0.75(1). We provide evidence for the continuous degradation of the quasiparticle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally, we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction U, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.