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Nematic Quantum Criticality in Dirac Systems.

Jonas Schwab1, Lukas Janssen2, Kai Sun3

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We studied quantum phase transitions in Dirac fermion models. Both models showed continuous transitions, but with slow-approaching fixed points and significant velocity anisotropies in the quantum critical regime.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Theoretical Physics

Background:

  • Nematic quantum phase transitions are crucial for understanding exotic quantum states.
  • Dirac fermion models provide a platform to study fundamental quantum phenomena.
  • Lattice rotational symmetries play a key role in dictating phase behaviors.

Purpose of the Study:

  • Investigate nematic quantum phase transitions in two distinct Dirac fermion models.
  • Analyze the impact of twofold and fourfold lattice rotational symmetries.
  • Characterize the quantum critical regime and its properties.

Main Methods:

  • Utilized negative-sign-free quantum Monte Carlo simulations.
  • Employed an epsilon-expansion renormalization group analysis.
  • Examined models with spontaneous breaking of lattice rotational symmetries.

Main Results:

  • Both Dirac fermion models exhibit continuous phase transitions.
  • The quantum critical regime is marked by substantial velocity anisotropies.
  • Fixed-point values are approached exceptionally slowly, deviating from generic Gross-Neveu models.
  • Quasiuniversal regimes, not the infrared fixed point, characterize numerical and experimental findings.

Conclusions:

  • Nematic quantum phase transitions in these Dirac fermion models are continuous.
  • Velocity anisotropy is a defining characteristic of the slow-driven quantum critical regime.
  • Understanding quasiuniversal regimes is essential for interpreting experimental and numerical data in these systems.