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Quantum Monte Carlo Method in the Steady State.

A Erpenbeck1, E Gull1, G Cohen2,3

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.

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|May 19, 2023
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Summary
This summary is machine-generated.

We developed a new steady-state inchworm Monte Carlo method for quantum impurity models. This approach significantly reduces computational costs and provides new insights into correlated materials under bias voltage.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Computational physics

Background:

  • Nonequilibrium quantum impurity models are computationally challenging.
  • Simulating steady-state dynamics requires efficient numerical methods.

Purpose of the Study:

  • To introduce a numerically exact steady-state inchworm Monte Carlo method.
  • To enable efficient simulation of nonequilibrium quantum impurity models.
  • To explore the response of correlated materials to external bias.

Main Methods:

  • Steady-state inchworm Monte Carlo algorithm.
  • Direct formulation in the steady state, avoiding transient dynamics.
  • Application to quantum dots and dynamical mean-field theory (DMFT) models.

Main Results:

  • The method provides access to larger parameter regimes at reduced computational cost.
  • Benchmarking on quantum dots in noninteracting and Kondo regimes.
  • Qualitative differences observed in the response of correlated materials compared to quantum dots.

Conclusions:

  • The steady-state method is a powerful tool for nonequilibrium quantum impurity models.
  • It offers significant computational advantages over traditional methods.
  • The study reveals distinct responses of correlated materials and quantum dots to bias voltage.