| Preface | p. vii |
| Overview | p. 1 |
| Orientation | p. 1 |
| An experiment--ballistic expansion | p. 6 |
| One dimension versus two or three dimensions | p. 8 |
| Quantum mechanics | p. 12 |
| The essence of the Bethe ansatz | p. 12 |
| A simple example--the 1/r[superscript 2] potential | p. 15 |
| References and history | p. 18 |
| Integrability and Nondiffraction | p. 27 |
| What does it mean to say that a system is integrable? | p. 27 |
| Scattering without diffraction | p. 30 |
| Proof of integrability for the hyperbolic potential | p. 36 |
| The potentials | p. 36 |
| Proof of integrability | p. 38 |
| The asymptotic momenta are conserved | p. 42 |
| The [delta]-function potential | p. 44 |
| Adding periodic boundary conditions | p. 45 |
| This is not a low-density approximation | p. 49 |
| Techniques | p. 53 |
| Our fundamental equation | p. 53 |
| The ground state | p. 54 |
| Response of the ground state | p. 61 |
| Excitations near the ground state | p. 64 |
| Zero-temperature thermodynamics | p. 68 |
| Finite temperature thermodynamics | p. 70 |
| The inverse-square potential--an example | p. 72 |
| The Classical Limit | p. 75 |
| Classical diffraction--pictures from an exhibition | p. 75 |
| The classical limit | p. 90 |
| Classical system at zero temperature | p. 93 |
| The inverse-square limit--example 1 | p. 95 |
| The Toda limit--example 2 | p. 97 |
| Solitons and constant profile solutions | p. 100 |
| Groundstate Wavefunctions of Product Form | p. 102 |
| An ansatz for the ground state wavefunction | p. 102 |
| Motivation for the product form | p. 103 |
| An inverse problem | p. 104 |
| The trigonometric case | p. 106 |
| Details | p. 108 |
| Excited states for the trigonometric case | p. 109 |
| Summary | p. 109 |
| A transformation | p. 110 |
| Change of basis | p. 111 |
| Off-diagonal elements of H' | p. 113 |
| Energy eigenvalues | p. 114 |
| Validity of the asymptotic Bethe ansatz | p. 115 |
| An example | p. 116 |
| Ground state correlations for the trigonometric case | p. 116 |
| The normalization constant | p. 116 |
| Analogy with a classical plasma | p. 118 |
| Important correlation functions | p. 119 |
| Correlations for special values of [lambda] | p. 123 |
| The Heisenberg-Ising Model | p. 131 |
| The model and its symmetries | p. 131 |
| The model | p. 131 |
| Rotational symmetry | p. 132 |
| Translational symmetry | p. 132 |
| Ground state in the thermodynamic limit | p. 133 |
| Other models | p. 134 |
| Quantum lattice gas | p. 134 |
| Statistics of the lattice gas | p. 135 |
| Twisted lattice gas | p. 137 |
| What we are going to find--a preview | p. 138 |
| Bethe's ansatz | p. 143 |
| The wavefunction | p. 143 |
| Well-separated particles | p. 143 |
| Near-neighbors | p. 144 |
| Two-body phase shift [theta] | p. 145 |
| Periodic boundary conditions | p. 145 |
| Twisted boundary conditions and recapitulation | p. 146 |
| The dilute limit M [double less-than sign] N | p. 146 |
| M = 0 | p. 146 |
| M = 1 | p. 146 |
| M = 2 | p. 148 |
| A change of variables | p. 154 |
| [Delta less than sign] -1, antiferromagnet | p. 154 |
| 1 [greater than sign Delta greater than sign] -1, paramagnet | p. 155 |
| [Delta] = -1, Heisenberg antiferromagnet | p. 155 |
| The ground state | p. 157 |
| Preliminaries | p. 157 |
| Half-filled lattice | p. 158 |
| [Delta] = -cosh [lambda less than sign] -1, antiferromagnet | p. 159 |
| 1 [greater than sign Delta] = -cos [mu greater than sign] -1, paramagnet | p. 160 |
| [Delta] = -1, Heisenberg antiferromagnet | p. 161 |
| Perturbations and excitations of the ground state | p. 161 |
| The general results | p. 162 |
| Half-filling | p. 166 |
| [Delta less than sign] -1, antiferromagnet | p. 167 |
| 1 [greater than sign Delta greater than sign] -1, paramagnet | p. 168 |
| [Delta] = -1, Heisenberg antiferromagnet | p. 168 |
| Zero-temperature thermodynamics | p. 170 |
| Fundamental integral equation | p. 170 |
| Near half-filling | p. 171 |
| The function [kappa] | p. 172 |
| Evaluation for the paramagnet | p. 174 |
| Evaluation for the antiferromagnet | p. 177 |
| What do our calculations really mean? | p. 178 |
| The low-density limit and complex solutions | p. 180 |
| M-strings | p. 180 |
| Dispersion relations | p. 182 |
| Boosting the bound states | p. 184 |
| Further results | p. 186 |
| Consistency | p. 189 |
| How can we show integrability? | p. 189 |
| The direct approach | p. 189 |
| The constructive approach | p. 190 |
| The indirect approach | p. 192 |
| How can we show non-integrability? | p. 193 |
| Consistency conditions | p. 197 |
| Solution to consistency conditions | p. 205 |
| Two components, conjugation symmetry | p. 205 |
| Consistency conditions | p. 205 |
| Necessary conditions for r and t | p. 208 |
| Bound states | p. 210 |
| Two components, different statistics | p. 213 |
| Three or more components | p. 215 |
| Periodic and twisted boundary conditions | p. 217 |
| Eigenvectors of the transfer matrix, two-components | p. 220 |
| The basic equations | p. 220 |
| The winding matrix and the transfer operator | p. 222 |
| Twisted boundary conditions | p. 224 |
| Properties of the winding matrix and the transfer operator | p. 225 |
| Eigenvalues | p. 228 |
| Explicit expressions for the equations | p. 230 |
| Solution to the general problem | p. 231 |
| Eigenvectors of the transfer matrix: multicomponent system | p. 232 |
| Basic equations | p. 233 |
| The winding matrix and the transfer operator | p. 235 |
| Properties of the winding matrix and the transfer operator | p. 236 |
| Eigenvalues | p. 238 |
| Summary of results | p. 242 |
| The constructive approach | p. 242 |
| Exchange Models | p. 244 |
| Hyperbolic exchange models | p. 245 |
| Integrability | p. 246 |
| The two-body phase shifts | p. 248 |
| The inverse-square exchange potential | p. 249 |
| The [delta]-function potential | p. 253 |
| The case F[superscript 2]--repulsive | p. 254 |
| The case B[superscript 2] | p. 256 |
| The case F[superscript 2]--attractive | p. 258 |
| The case BF | p. 261 |
| The Sinh-Cosh Model | p. 262 |
| The sinh-cosh potential | p. 262 |
| Integrability | p. 263 |
| The two-body problem | p. 265 |
| Phase shifts | p. 267 |
| Spin waves | p. 269 |
| Solution and results for zero temperature and zero spin/charge | p. 270 |
| Exchange Lattice Systems by Freezing | p. 275 |
| Freezing continuum models to give lattice models | p. 275 |
| Review of the continuum exchange model | p. 277 |
| The limit [lambda] to [infinity] | p. 279 |
| The first order equation | p. 280 |
| The densities [rho](x) and e(x) | p. 282 |
| Results for the nearest-neighbor model | p. 284 |
| Results for the hyperbolic model | p. 286 |
| The inverse-square lattice at finite temperature | p. 289 |
| The Hubbard Model | p. 295 |
| The model and its symmetries | p. 295 |
| The model | p. 295 |
| Other statistics | p. 296 |
| The phase diagram and symmetries | p. 298 |
| Bethe's ansatz | p. 299 |
| The wavefunction | p. 299 |
| Well-separated particles | p. 300 |
| Double occupancy | p. 300 |
| Two-body scattering amplitudes | p. 302 |
| A change of variables | p. 303 |
| The repulsive case | p. 304 |
| The fundamental equations | p. 304 |
| The ground state | p. 305 |
| The attractive case | p. 308 |
| The bound state | p. 308 |
| Consistency conditions and the scattering of pairs | p. 312 |
| A fluid of pairs | p. 313 |
| Ground state properties at the symmetric point | p. 314 |
| Excitations at the symmetric point | p. 314 |
| Ground state response | p. 314 |
| Holes and particles in the fluid of pairs | p. 315 |
| Unbound particles | p. 316 |
| Some Two-Body Problems | p. 319 |
| The two-body problem | p. 319 |
| The potential v(r) = c[delta](r) | p. 324 |
| The potential v(r) = [lambda]([lambda] - 1)/r[superscript 2] | p. 326 |
| The potential v(r) = [lambda]([lambda] - 1)/sinh[superscript 2]r | p. 327 |
| The potential v(r) = -[lambda]([lambda] - 1)/cosh[superscript 2]r | p. 331 |
| Combination potentials | p. 336 |
| Representations | p. 338 |
| The permutation group | p. 338 |
| The twisted permutation group | p. 342 |
| Two ways to write the Bethe ansatz | p. 345 |
| Two-body scattering | p. 347 |
| The consistency conditions | p. 349 |
| Representations | p. 350 |
| Twisted boundary conditions | p. 353 |
| Realizations | p. 360 |
| Lattice gases | p. 360 |
| Other realizations | p. 363 |
| Nearest-neighbor hopping | p. 365 |
| Periodic boundary conditions | p. 368 |
| Bibliography | p. 371 |
| Index | p. 377 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
