| Preface |
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xi | |
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1 | (18) |
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1 | (2) |
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One-dimensional interaction as a disguise |
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3 | (1) |
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Two-body problem with 1/r2 interaction |
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4 | (6) |
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10 | (1) |
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From spin permutation to graded permutation |
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11 | (2) |
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13 | (3) |
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16 | (3) |
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Part I Physical properties |
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19 | (290) |
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Single-component Sutherland model |
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21 | (77) |
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22 | (10) |
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Jastrow-type wave functions |
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22 | (2) |
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Triangular matrix for Hamiltonian |
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24 | (6) |
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Ordering of basis functions |
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30 | (2) |
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Descriptions of energy spectrum |
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32 | (4) |
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Interacting boson description |
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32 | (2) |
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Interacting fermion description |
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34 | (1) |
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34 | (2) |
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36 | (11) |
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37 | (3) |
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40 | (3) |
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43 | (2) |
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45 | (2) |
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47 | (8) |
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Interacting boson picture |
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48 | (2) |
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50 | (1) |
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Exclusion statistics and duality |
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51 | (3) |
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Elementary excitation picture |
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54 | (1) |
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Introduction to Jack polynomials |
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55 | (6) |
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Dynamics in thermodynamic limit |
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61 | (9) |
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Hole propagator <ψ†(x, t)ψ(0,0)> |
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62 | (3) |
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Particle propagator <ψ(x, t)ψ†(0,0)> |
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65 | (2) |
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Density correlation function |
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67 | (3) |
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Derivation of dynamics for finite-sized systems |
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70 | (20) |
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71 | (6) |
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77 | (9) |
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Density correlation function |
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86 | (4) |
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Reduction to Tomonaga-Luttinger liquid |
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90 | (8) |
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Asymptotic behavior of correlation functions |
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91 | (2) |
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93 | (5) |
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Multi-component Sutherland model |
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98 | (52) |
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Triangular form of Hamiltonian |
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99 | (5) |
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Energy spectrum of multi-component fermionic model |
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104 | (7) |
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Eigenstates of identical particles |
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104 | (3) |
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Wave function of ground state |
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107 | (2) |
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Eigenstates with bosonic Fock condition |
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109 | (2) |
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Energy spectrum with most general internal symmetry |
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111 | (3) |
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114 | (6) |
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114 | (1) |
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115 | (5) |
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120 | (9) |
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Multi-component bosons and fermions |
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120 | (3) |
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Explicit results for U(2) anyons |
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123 | (4) |
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Generalization to U(K) symmetry |
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127 | (2) |
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129 | (6) |
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Non-symmetric Jack polynomials |
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129 | (4) |
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Jack polynomials with U(2) symmetry |
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133 | (2) |
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Dynamics of U(2) Sutherland Model |
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135 | (7) |
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Hole propagator <ψ†↓(x, t)ψ↓(0,0)> |
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136 | (2) |
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Unified description of correlation functions |
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138 | (4) |
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Derivation of dynamics for finite-sized systems |
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142 | (8) |
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142 | (4) |
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Density correlation function |
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146 | (4) |
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Spin chain with 1/r2 interactions |
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150 | (70) |
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Mapping to hard-core bosons |
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151 | (1) |
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Gutzwiller-Jastrow wave function |
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152 | (4) |
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Hole representation of lattice fermions |
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152 | (3) |
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Gutzwiller wave function in Jastrow form |
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155 | (1) |
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Projection to the Sutherland model |
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156 | (1) |
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157 | (6) |
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Derivation of static correlation functions |
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163 | (8) |
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171 | (2) |
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173 | (7) |
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173 | (2) |
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175 | (3) |
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178 | (2) |
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Energy levels and their degeneracy |
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180 | (8) |
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Degeneracy beyond SU(2) symmetry |
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180 | (3) |
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183 | (2) |
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185 | (3) |
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From Young diagrams to ribbons |
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188 | (8) |
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188 | (2) |
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Completeness of spinon basis |
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190 | (3) |
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Semionic statistics of spinons |
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193 | (1) |
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Variants of Young diagrams |
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194 | (2) |
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196 | (12) |
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Energy functional of spinons |
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196 | (4) |
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Thermodynamic potential of spinons |
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200 | (3) |
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Susceptibility and specific heat |
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203 | (2) |
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Thermodynamics by freezing trick |
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205 | (3) |
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Dynamical structure factor |
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208 | (12) |
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Brief survey on dynamical theory |
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208 | (3) |
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211 | (4) |
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Dynamics in magnetic field |
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215 | (4) |
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Comments on experimental results |
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219 | (1) |
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220 | (13) |
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Coordinate representation of ground state |
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221 | (2) |
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223 | (6) |
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Statistical parameters via freezing trick |
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229 | (2) |
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Dynamical structure factor |
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231 | (2) |
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Supersymmetric t-J model with 1/r2 interaction |
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233 | (76) |
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Global supersymmetry in t---J model |
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234 | (1) |
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Mapping to U(1,1) Sutherland model |
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235 | (4) |
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239 | (6) |
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Spectrum of elementary excitations |
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245 | (11) |
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Energy of polynomial wave functions |
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245 | (5) |
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250 | (3) |
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253 | (3) |
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256 | (6) |
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256 | (3) |
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Ribbon diagrams and supermultiplets |
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259 | (2) |
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Motif as representation of supermultiplets |
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261 | (1) |
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262 | (16) |
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Parameters for exclusion statistics |
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262 | (3) |
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Energy and thermodynamic potential |
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265 | (2) |
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267 | (1) |
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Distribution functions at low temperature |
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268 | (2) |
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270 | (2) |
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272 | (2) |
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Entropy and specific heat |
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274 | (4) |
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Dynamics of supersymmetric t---J model |
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278 | (24) |
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Coupling of external fields to quasi-particles |
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278 | (2) |
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Dynamical spin structure factor |
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280 | (7) |
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Dynamical structure factor in magnetic fields |
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287 | (3) |
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Dynamical charge structure factor |
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290 | (3) |
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Electron addition spectrum |
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293 | (2) |
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Electron removal spectrum |
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295 | (5) |
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300 | (2) |
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Derivation of dynamics for finite-sized t-J model |
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302 | (7) |
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Electron addition spectrum |
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303 | (3) |
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Dynamical spin structure factor |
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306 | (3) |
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Part II Mathematics related to 1/r2 systems |
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309 | (146) |
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311 | (80) |
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Non-symmetric Jack polynomials |
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312 | (22) |
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312 | (2) |
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Cherednik-Dunkl Operators |
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314 | (5) |
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Definition of non-symmetric Jack polynomials |
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319 | (1) |
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319 | (5) |
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324 | (5) |
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Arms and legs of compositions |
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329 | (4) |
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333 | (1) |
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Antisymmetrization of Jack polynomials |
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334 | (12) |
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Antisymmetric Jack polynomials |
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334 | (4) |
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338 | (3) |
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341 | (1) |
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342 | (4) |
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Symmetric Jack polynomials |
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346 | (25) |
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Relation to non-symmetric Jack polynomials |
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346 | (5) |
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351 | (1) |
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Symmetry-changing operator |
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352 | (3) |
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Bosonic description of partitions |
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355 | (4) |
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359 | (1) |
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360 | (4) |
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364 | (1) |
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364 | (1) |
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365 | (3) |
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Skew Jack functions and Pieri formula |
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368 | (3) |
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371 | (11) |
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Relation to non-symmetric Jack polynomials |
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371 | (1) |
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372 | (1) |
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Cauchy product expansion formula |
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373 | (1) |
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373 | (2) |
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375 | (2) |
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377 | (4) |
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381 | (1) |
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382 | (9) |
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Relation to non-symmetric Jack polynomials |
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382 | (2) |
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384 | (1) |
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Bosonization for separated states |
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385 | (1) |
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Factorization for separated states |
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386 | (2) |
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Binomial formula for separated states |
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388 | (1) |
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389 | (2) |
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Yang---Baxter relations and orthogonal eigenbasis |
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391 | (31) |
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Fock condition and R-matrix |
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392 | (5) |
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R-matrix and monodromy matrix |
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397 | (4) |
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401 | (2) |
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Relation to U(2) Sutherland model |
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403 | (3) |
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Construction of orthogonal set of eigenbasis |
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406 | (13) |
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Examples for small systems |
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406 | (10) |
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Orthogonal eigenbasis for N-particle systems |
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416 | (3) |
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Norm of Yangian Gelfand-Zetlin basis |
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419 | (3) |
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SU(K) and supersymmetric Yangians |
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422 | (19) |
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Construction of monodromy matrix |
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423 | (3) |
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Quantum determinant vs. ordinary determinant |
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426 | (1) |
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427 | (3) |
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Quantum determinant of SU(K) Yangian |
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430 | (1) |
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Alternative construction of monodromy matrix |
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431 | (4) |
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435 | (3) |
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Extension to supersymmetry |
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438 | (3) |
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441 | (14) |
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Macdonald symmetric polynomials |
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441 | (3) |
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444 | (1) |
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Reduction to single-component bosons |
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445 | (4) |
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From Yangian Gelfand-Zetlin basis to Uglov polynomials |
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449 | (1) |
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Dynamical correlation functions |
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450 | (5) |
| Afterword |
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455 | (3) |
| References |
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458 | (6) |
| Index of symbols |
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464 | (7) |
| Index |
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471 | |
