Introduction to the auxiliary field quantum Monte Carlo method

Advanced course given by Natanael De Carvalho Costa, Sandro Sorella

Term: 3

Start: 15-04-2020 End: 07-05-2020 Room: 131

Credits: 2

Schedule: Wed 14:00 - 16:30, Thu 14:00 - 16:30

Program

1 -- The auxiliary-field quantum Monte Carlo method

1.1 Trotter decomposition: World-line approach
1.2 Hubbard-Stratonovich transformation
1.3 Determinantal weights and the minus-sign problem
1.4 The zero-temperature approach

2 -- Algorithm details

2.1 Greens' function measurements
2.2 Fast updates
2.3 Physical observables
2.4 Matrix-decomposition stabilization

3 -- Applications

3.1 The Hubbard model
3.2 The periodic Anderson model
3.3 The Holstein model
3.4 The Hubbard-Holstein model

4 -- Hands-on the AFQMC code
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