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Fermions at Finite Density in 2+1 Dimensions with Sign-Optimized Manifolds.

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This summary is machine-generated.

Monte Carlo simulations reveal that high densities and temperatures abruptly reduce the chiral condensate in the (2+1)-dimensional Thirring model. This study overcomes the sign problem using complexified path integrals.

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Area of Science:

  • Quantum Field Theory
  • Statistical Mechanics
  • High Energy Physics

Background:

  • The Thirring model is a fundamental model in quantum field theory.
  • Studying its thermodynamics at finite density is crucial for understanding strongly interacting systems.
  • The sign problem in lattice simulations hinders calculations at finite density.

Purpose of the Study:

  • To perform Monte Carlo calculations of the thermodynamics of the (2+1)-dimensional Thirring model at finite density.
  • To overcome the sign problem in lattice simulations.
  • To investigate the behavior of the chiral condensate under varying density and temperature conditions.

Main Methods:

  • Utilized Monte Carlo calculations.
  • Employed a novel approach by deforming the path integral domain into complex space to maximize the average sign.
  • Performed calculations on lattice sizes up to 10^3.

Main Results:

  • Successfully bypassed the sign problem in (2+1)-dimensional Thirring model simulations.
  • Observed an abrupt reduction in the chiral condensate at high densities and/or temperatures.
  • Provided thermodynamic data for the model at finite density.

Conclusions:

  • The complexified path integral method is effective for tackling the sign problem.
  • Finite density and temperature significantly impact the chiral condensate in this model.
  • The findings offer insights into the phase structure of quantum field theories at finite density.