TY - JOUR

T1 - Single-particle Green's functions of the Calogero-Sutherland model at couplings λ=1/2, 1, and 2

AU - Zirnbauer, M. R.

AU - Haldane, F. D.M.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1995

Y1 - 1995

N2 - At coupling strengths λ=1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction with superanalytic techniques developed in mesoscopic conductor physics, we derive an exact integral representation for the CSM two-particle Green's function in the thermodynamic limit. Simple closed expressions for the single-particle Green's functions are extracted by separation of points. For the advanced part, where a particle is added to the ground state and later removed, a sum of two contributions is found: the expected one, with just one particle excitation present, plus an extra term arising from fractionalization of the single particle into a number of elementary particle and hole excitations.

AB - At coupling strengths λ=1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction with superanalytic techniques developed in mesoscopic conductor physics, we derive an exact integral representation for the CSM two-particle Green's function in the thermodynamic limit. Simple closed expressions for the single-particle Green's functions are extracted by separation of points. For the advanced part, where a particle is added to the ground state and later removed, a sum of two contributions is found: the expected one, with just one particle excitation present, plus an extra term arising from fractionalization of the single particle into a number of elementary particle and hole excitations.

UR - http://www.scopus.com/inward/record.url?scp=18744415582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18744415582&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.52.8729

DO - 10.1103/PhysRevB.52.8729

M3 - Article

AN - SCOPUS:18744415582

VL - 52

SP - 8729

EP - 8746

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 12

ER -