Physics in one dimension: theoretical concepts for quantum many-body systems

Abstract

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

Invited introductory theoretical paper in a JPCM special issue on physics in one dimension

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Universal theory of nonlinear Luttinger liquids
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Nuclear Magnetism and Electronic Order in 13C Nanotubes
• Electron transport in disordered Luttinger liquid

Cited by in corpus (9)

• One-dimensional quantum antiferromagnetism in the $p-$orbital CsO${}_2$ compound revealed by electron paramagnetic resonance
• Approaching Many-Body Localization from Disordered Luttinger Liquids via the Functional Renormalization Group
• Phase diagram of doped BaFe${}_2$As${}_2$ superconductor under broken $C_4$ symmetry
• Time evolution during and after finite-time quantum quenches in Luttinger liquids
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• 1D half-filled paramagnetic Hubbard model.The Luttinger critical exponents