Abstract
We investigate a polaronic excitation in a one-dimensional spin-1/2 Fermi gas with contact attractive interactions, using the complex Langevin method, which is a promising approach to evade a possible sign problem in quantum Monte Carlo simulations. We found that the complex Langevin method works correctly in a wide range of temperature, interaction strength, and population imbalance. The Fermi polaron energy extracted from the two-point imaginary Green's function is not sensitive to the temperature and the impurity concentration in the parameter region we considered. Our results show a good agreement with the solution of the thermodynamic Bethe ansatz at zero temperature.
Highlights
The quantum Monte Carlo method [1,2] is widely used in various fields of physics as a nonperturbative tool of analysis
The positivity of the Boltzmann weight is violated in many physically interesting systems: the Hubbard model, finite density quantum chromodynamics (QCD), QCD with a θ term, matrix superstring models, and any systems defined by the Schwinger-Keldysh formalism which describes real-time dynamics, for instance [3,4,5,6,7,8,9,10]
We have studied the excitation properties of Fermi polarons at finite temperature for the attractive Gaudin-Yang model with large population imbalances using the complex Langevin method, a nonperturbative approach free from the sign problem
Summary
The quantum Monte Carlo method [1,2] is widely used in various fields of physics as a nonperturbative tool of analysis. The positivity of the Boltzmann weight is violated in many physically interesting systems: the Hubbard model, finite density quantum chromodynamics (QCD), QCD with a θ term, matrix superstring models, and any systems defined by the Schwinger-Keldysh formalism which describes real-time dynamics, for instance [3,4,5,6,7,8,9,10]. In these cases, the number of samples becomes exponentially large as the system size grows in order to obtain statistically significant results.
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