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Exact results of the one-dimensional repulsive Hubbard model
Jia-Jia Luo1,2, Han Pu3, Xi-Wen Guan1,4,5,6
1Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China.
Reports on Progress in Physics. Physical Society (Great Britain)
|September 16, 2024
Summary
This study analyzes the one-dimensional Hubbard model, revealing fractionalized excitations and quantum criticality. It provides analytical insights into thermodynamic properties and spin-incoherent Luttinger liquids, guiding future experiments.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Statistical Mechanics
Background:
- The one-dimensional (1D) Hubbard model is a fundamental model for understanding interacting electrons in low dimensions.
- Investigating its properties under external fields and at quantum criticality is crucial for condensed matter physics.
Purpose of the Study:
- To present analytical results for the fundamental properties of the 1D Hubbard model with repulsive interactions under arbitrary external fields.
- To elucidate quantum criticality, fractionalized excitations, and thermodynamic properties.
- To provide a comprehensive understanding of quantum phase transitions and their relation to experimental systems.
Main Methods:
- Exact solutions of the Bethe ansatz equations for the Hubbard model.
- Analytical calculation of gapless and gapped excitations (spinons, holons, magnons, eta-pairs).
- Application of conformal field theory and analysis of two-point correlation functions.
Main Results:
- Rigorous calculation of fractionalized spin and charge excitations (spinons and holons).
- Analytical determination of thermodynamic properties, dimensionless ratios, and scaling functions near quantum phase transitions.
- Elucidation of the spin-incoherent Luttinger liquid (SILL) and its thermodynamics.
- Proposal of an adiabatic cooling scheme based on quantum criticality and Mott insulators.
Conclusions:
- The study provides a comprehensive understanding of quantum criticality in the 1D Hubbard model.
- The analytical methods and results offer insights into quantum integrability and guide experiments with interacting electrons and ultracold atoms.
- New perspectives on Mott insulators and interaction-driven criticality are presented.
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