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Fourth- and Fifth-Order Virial Coefficients from Weak Coupling to Unitarity
1Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
Physical Review Letters
|August 16, 2020
Summary
Researchers calculated universal virial coefficients for the spin-1/2 Fermi gas, providing new predictions for b5 and refining understanding of strongly correlated quantum systems.
Area of Science:
- Quantum Many-Body Physics
- Statistical Mechanics
- Atomic, Molecular, and Optical Physics
Background:
- The unitary limit of the nonrelativistic spin-1/2 Fermi gas is a key system in quantum many-body physics.
- Its thermodynamics depend on universal functions and virial coefficients (b_n) that describe n-body effects.
- While b2 and b3 are understood, b4 and b5 require further investigation.
Purpose of the Study:
- To determine the interaction-induced change in virial coefficients (Δb_n) from weak coupling to unitarity.
- To provide predictions for b4 and b5 in the strongly correlated Fermi gas.
- To analyze the impact of these coefficients on the system's equation of state and Tan contact.
Main Methods:
- Implementation of a nonperturbative analytic approach.
- Utilizing Trotter-Suzuki factorization of the imaginary-time evolution operator.
- Employing progressively finer temporal lattice spacings and automated algebra codes.
Main Results:
- Calculated Δb3 = -0.356(4), consistent with prior results.
- Determined Δb4 = 0.062(2), aligning with theoretical estimates but differing from experimental data.
- Predicted Δb5 = 0.078(6) for the first time.
- Demonstrated the influence of these coefficients on the density equation of state and Tan contact.
Conclusions:
- The study provides crucial, high-precision values for virial coefficients of the Fermi gas.
- The findings offer new insights into the behavior of strongly correlated quantum systems.
- Discrepancies with experimental results for Δb4 warrant further investigation.
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