1	Numerical Renormalisation Group and the Metal-Insulator Transition in Disordered Systems Angus MacKinnon Imperial College London
2	Acknowledgements Bernhard Kramer, Michael Schreiber, Keith Slevin, Tomi Ohtsuki, Isa Zarakheshev, Rudolf Römer, Kohei Itoh Etienne Hofstetter, John Taylor, Alex Taylor, Jonathan Carter
3	The Anderson Hamiltonian
4	Mobility Edge
5	Universality Classes The original 3 Orthogonal spinless time-reversal symmetric Unitary broken time-reversal symmetry Static or random magnetic field Symplectic spin-orbit coupling The others Bogoliubov-de Gennes Superconductivity ……
6	Critical Behaviour
7	Numerical Methods (a) Transfer Matrix
8	Data Analysis
9	Fitted Data
10	Conductance Fit
11	Numerical Methods (b) Level Spacing
12	Scaling of level spacing distribution
13	Experiment Neutron transmutation doping (Kohei Itoh et al.)
14	Experiment Neutron Transmutation Doping
15	Experiment 2 Same Ge:Ga Boundary depends on compensation.
16	Summary so far Critical exponent can be calculated accurately: s = 1.58 Experiments now give good temperature driven scaling: s=1.0 What about 2D at low density? What is wrong? Theory and/or Numerics wrong? Experiments wrong? Something missing? Interactions? Good agreement between theory and experiment for QHE system only.
17	Interacting Electrons Number of states scales as 2^N rather than N Possible Approaches: Recursive Green’s function like Exact representation including all states Not yet possible Density Matrix Renormalisation Group like Some results Hubbard-Stratonovich like d+1 dimensions
18	Spinless Electrons in 1D
19	Delocalisation in 1D
20	Conclusions Critical exponent for non-interacting systems can be evaluated accurately and reproducibly: 1.58 Experimental results becoming more reliable, but critical exponent = 1.0 Need calculations with disorder and interactions. Initial steps being made.
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