Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems

By Jorge Dukelsky, Stuart Pittel, Germán Sierra. 2004

288 citations recorded by the source corpus.

The use of exactly solvable Richardson-Gaudin models to describe the physics of systems with strong pair correlations is reviewed. The article begins with a brief discussion of Richardson's early work, which demonstrated the exact solvability of the pure pairing model, and then shows how that work has evolved recently into a much richer class of exactly solvable models. The Richardson solution leads naturally to an exact analogy between these quantum models and classical electrostatic problems in two dimensions. This analogy is then used to demonstrate formally how BCS theory emerges as the large-$N$ limit of the pure pairing Hamiltonian. Several applications to problems of relevance to condensed-matter physics, nuclear physics, and the physics of confined systems are considered. Some of the interesting effects that are discussed in the context of these exactly solvable models include (i) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains; (ii) the role of the nucleon Pauli principle in suppressing the effects of high-spin bosons in interacting boson models of nuclei, and (iii) the possibility of fragmentation in confined boson systems. Interesting insight is also provided into the origin of the superconducting phase transition both in two-dimensional electronic systems and in atomic nuclei, based on the electrostatic image of the corresponding exactly solvable quantum pairing models.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/e2730464c53e9b27c74ef5f52e5d5e80ce8699a6

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Entanglement in many-body systems (2007, methodology): “Both the LMG and the BCS type models can be solved exactly by Bethe Ansatz (Richardson, 1963; Richardson and Sherman, 1964) (see also Dukelsky et al., 2004 for a review) as they are quasi classical descendants of the six vertex model (Amico et al., 2001; Di Lorenzo et al., 2002; Ortiz et al., 2005).”
Comparing and contrasting nuclei and cold atomic gases (2013, methodology): “Schematic and exactly solvable pairing models have also been studied in great detail (Dukelsky et al. 2004, Pan & Draayer 1999).”
Fermi gases in one dimension: From Bethe ansatz to experiments (2013, methodology): “The traditional s-wave BCS pairing models have various applications to problems in condensed matter physics (Dukelsky et al., 2004; Links et al., 2003; Ying et al., 2008a,b), nuclear physics (Pan and Draayer, 2002) and ultrasmall metallic grains (von Delft and Ralph, 2001) etc.”