Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Heßelmann, Stephan; Lang, Thomas C.; Schuler, Michael; Wessel, Stefan; Läuchli, Andreas M.

doi:10.1126/science.aav6869

Cited by 11 publications

(9 citation statements)

References 5 publications

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“…Based on this result, we suppose that the increase of v F tends to enhance M but at the same time the magnetic catalysis generating fermion mass does to suppress it, and as a result of this cancellation, M remains almost unchanged for small V . Note that a similar effect is expected in a real Dirac material, where a long-range part of the Coulomb interaction could suppress the diamagnetism via the magnetic catalysis at zero temperature with a partial cancellation by the enhanced Fermi velocity 12 , although it is expected to be less important when the short-range interaction is strong enough 38,43,[54][55][56] . As the magnetic field becomes stronger, |M (V = 0.5t)| becomes even larger than |M (V = 0)| within the present model calculation.…”

Section: Numerical Resultsmentioning

confidence: 57%

“…54, ν 0.80 corresponding to the N = 4 chiral Ising universality class. Note that, if present, the long-range part of the Coulomb interaction is less important around the QCP and does not affect the criticality at zero magnetic field 38,43,[54][55][56] . Because the system is gapped at B = 0 for any V > 0 due to the magnetic catalysis, the iDMRG numerical calculations with finite bond dimensions χ are stable and extrapolation χ → ∞ works well.…”

Section: Modelmentioning

confidence: 99%

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Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

Tada¹

2021

Preprint

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We study orbital diamagnetism in (2 + 1)-dimensional Dirac electrons with a short-range interaction at zero temperature. We introduce orbital magnetic fields into spinless Dirac electrons on the π-flux sqaure lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact when the short-range interaction V is weak, while it is monotonically suppressed for larger interactions. Around the quantum critical point (QCP) of a charge density wave phase transition, we find a scaling behavior of the ground state energy density characteristic of the chiral Ising universality class. This leads to universal orbital diamagnetism in correlated Dirac electrons around the QCP, which may be regarded as a quantum, magnetic analogue of critical Casimiar effect which has been widely studied for classical phase transitions.

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Section: Numerical Resultsmentioning

confidence: 57%

Section: Modelmentioning

confidence: 99%

Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

Tada¹

2021

Preprint

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“…( 20), is thus particularly dangerous in the vicinity of interacting quantum critical points and a very careful analysis including proper finite-size scaling is necessary [13,37]. As pointed out recently [20], such a crossover due to enhanced finite-size shifts in the excitation gap at the Dirac point led the authors in Ref. [19] to drastically underestimate the Fermi velocity in the Hubbard model on the honeycomb lattice near its QCP.…”

Section: Quantifying the Fermi Velocity Renormalizationmentioning

confidence: 99%

“…Furthermore the study of the GNY field theory and the corresponding microscopic models allows us to clarify the crossover flow of the torus energy spectrum between two different infrared (IR) fixed points. This advance enables us to reliably measure the Fermi velocity, which is the condensed matter analogy of the speed of light of the GNY field theory, a topic of recent controversy [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

Schuler,

Hesselmann,

Whitsitt

et al. 2019

Preprint

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We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with nD = 4 component Dirac spinors in D = (2 + 1) dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or π-flux square lattice. The torus spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus spectrum analytically using the perturbative expansion in = 4 − D, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar orderparameter field strongly influences the critical torus spectrum. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

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“…The critical behaviors around a quantum critical point (QCP) of the semimetal-insulator phase transition have been well established mainly in absence of a magnetic field [35][36][37][38][39][40][41][42][43][44][45][46][47][48], and quantum criticality of magnetic catalysis can also be understood in a similar manner [49]. The scaling analysis shows that the Fermi velocity v F remains regular around a QCP [50], but numerical calculations demonstrate that v F decreases to some extent in interacting Dirac fermions which exhibit antiferromagnetic quantum phase transitions [51][52][53][54] and furthermore the reduced v F was observed in the molecular compound α-(BEDT-TTF) 2 I 3 [55]. Therefore, it is natural to expect suppression of diamagnetism in these systems similarly to the long-range Coulomb interacting graphene [15].…”

Section: Introductionmentioning

confidence: 99%

Robust orbital diamagnetism in correlated Dirac fermions

Tada

2022

New J. Phys.

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We study orbital diamagnetism at zero temperature in (2+1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point (QCP) of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.

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Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Cited by 11 publications

References 5 publications

Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

Robust orbital diamagnetism in correlated Dirac fermions

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