Partial Fermionization: Spectral Universality in 1D Repulsive Bose Gases

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Statistical mechanics

Background:

• The many-body level density is crucial for understanding spectral and thermodynamic properties of interacting quantum systems.
• Its smoothed form is particularly relevant due to its rapid growth with excitation energy.

Purpose of the Study:

• To compute the cumulative level density for confined one-dimensional continuous systems with repulsive short-range interactions.
• To demonstrate the universal behavior during the crossover from an ideal Bose gas to a strongly correlated, fermionized gas (partial fermionization).

Main Methods:

• Supplementing quantum cluster expansions with short-time dynamical information.
• Nonperturbative analytical calculations.
• Numerical simulations for validation.

Main Results:

• Demonstrated universal behavior in the crossover from ideal Bose gas to partial fermionization.
• Showed that systems with few and many particles share underlying spectral features.
• Achieved excellent agreement between analytical results and numerical data.

Conclusions:

• The derived method provides accurate predictions for excitation spectra.
• Enables access to finite-temperature thermodynamics across a wide range of parameters.
• Applicable to systems of experimental relevance in cold atom physics, including the Lieb-Liniger model and harmonically confined bosons.