This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Tomonaga–Luttinger liquid | |
|---|---|
| Name | Tomonaga–Luttinger liquid |
| Derived from | Tomonaga model; Luttinger model |
| Introduced by | Sin-Itiro Tomonaga; Joaquin Luttinger |
| Field | Condensed matter physics; Quantum many-body physics |
Tomonaga–Luttinger liquid The Tomonaga–Luttinger liquid is a theoretical paradigm describing interacting fermions in one-dimensional conductors, contrasting with the Fermi liquid paradigm of Lev Landau and John Bardeen. Originating from work by Sin-Itiro Tomonaga and later formalized by Joaquin Luttinger, the model underlies understanding of quantum wires, carbon nanotubes, and edge states in the quantum Hall effect. It provides exact predictions for power-law correlations, spectral functions, and transport, influencing research at institutions such as CERN, MIT, Bell Labs, and Max Planck Institute for the Physics of Complex Systems.
The model arose from attempts to extend field-theoretic techniques pioneered by Sin-Itiro Tomonaga and applied by Joaquin Luttinger to one-dimensional systems like the Luttinger model and the Tomonaga model. Subsequent developments by David Mattis, Daniel C. Mattis, and Elliott Lieb clarified solvable limits, while reviews by F. D. M. Haldane reframed the concept as a universal class applicable to models studied at University of Cambridge, Princeton University, and University of Illinois Urbana-Champaign. The framework competes with concepts from Lev Pitaevskii and Evgeny Lifshitz in many-body theory.
The formalism builds on second quantization methods introduced by Paul Dirac and uses linearization of dispersions around Fermi points, a technique related to approximations used by Richard Feynman and Hans Bethe in many-body problems. It replaces quasiparticle descriptions of Lev Landau with collective bosonic modes, an approach that draws on bosonization insights connected to work by John von Neumann and mathematical structures exploited by Satyendra Nath Bose and Albert Einstein. Parameters like the Luttinger parameter K and charge velocity v characterize universality classes; their computation employs techniques used by Elliott Lieb and Fabian H. L. Essler in integrable chains studied at University of Oxford and Université Paris-Sud.
Bosonization, promoted by F. D. M. Haldane and elaborated by Daniel C. Mattis and Alan Luther, maps fermionic operators to bosonic fields, a method paralleling canonical transformations used by Pascual Jordan and Eugene Wigner. Correlation functions show power-law decay with exponents set by K, reminiscent of scaling relations in works from Kenneth G. Wilson and Alexander Polyakov. Spectral functions and Green's functions derived via bosonization have been compared to exact results from Bethe ansatz studies by C. N. Yang and Chen-Ning Yang collaborators, and to renormalization group treatments developed at Stanford University and Cornell University.
Characteristic signatures include spin–charge separation first discussed by F. D. M. Haldane and observable as distinct modes akin to collective excitations studied in Peter W. Anderson's contexts, and power-law suppression or enhancement of tunneling as predicted in theoretical work echoing methods of Gian-Carlo Wick and Sin-Itiro Tomonaga. Transport anomalies, non-Fermi-liquid spectral features, and modified density of states informed experimental programs at IBM and Stanford Linear Accelerator Center. Predicted responses to impurities and boundary conditions connect to research by Imry Y. and Yigal Meir on mesoscopic conductors, and to mesoscopic experiments performed at University of Cambridge and Columbia University.
Realizations include quantum wires fabricated in GaAs heterostructures explored by teams at Bell Labs and IBM Thomas J. Watson Research Center, single-walled carbon nanotube measurements reported by groups at Rice University and Tsinghua University, and edge-state probes in the fractional quantum Hall effect pioneered by researchers at Princeton University and Weizmann Institute of Science. Cold-atom emulations using optical lattices by groups at MIT, Harvard University, and University of Bonn provide tunable interactions, while scanning tunneling spectroscopy experiments at Max Planck Institute for Solid State Research and Ecole Normale Supérieure have detected power-law tunneling consistent with predictions from the model.
Extensions include spinful Luttinger liquids studied in contexts linked to the Hubbard model and the Kondo effect as treated by Jun Kondo and Anderson Model analyses, helical Luttinger liquids relevant for topological insulator edges investigated at University of California, Berkeley and National Institute of Standards and Technology, and ladder systems connected to work on coupled chains by researchers at Tokyo Institute of Technology and Rice University. Related integrable models studied via Bethe ansatz include the XXZ model and the Calogero–Sutherland model, with cross-links to studies at Institute for Advanced Study and Steklov Institute of Mathematics.
Solvable limits exploit linear dispersion, bosonization, and refermionization techniques informed by the Bethe ansatz developed by Hans Bethe and extended by Richard J. Baxter. Renormalization group analyses trace conceptual lineage to Kenneth G. Wilson and implement flow equations akin to those used by Franz Wegner. Exact correlation functions in special cases have been obtained using methods by Elliott Lieb and collaborators and by exploiting conformal field theory approaches pioneered by Alexander Zamolodchikov and John Cardy, with applications discussed in seminars at Perimeter Institute and International Centre for Theoretical Physics.