Short description: This course offers an introduction to modern computational methods frequently used in the study of strongly-correlated many-body lattice systems in the field of condensed matter physics. Each method has its own area of expertise, with pros and cons. Topics include:
Overview of typical models : Hubbard model, Bose-Hubbard, transverse field Ising model, Heisenberg -, XY- and XXZ spin models
exact diagonalization : full diagonalizaton and Krylov based methods for sparse matrices, role of symmetries
primer to the density matrix renormalization group (DMRG) and matrix product states (MPS)
classical Monte Carlo simulations: basics of MC, phase transitions, cluster algorithms
quantum Monte Carlo simulation -- bosons : discrete and continuous time, worldline representation, SSE, worm algorithm
quantum Monte Carlo simulations -- fermions : determinant methods (BSS), diffusion Monte Carlo, variational methods
primer to neural network quantum states: architectures, training, and convergence
Requirements: introduction to programming, quantum mechanics, statistical physics, basic knowledge of typical condensed matter models
Recommended Textbooks:
Gubernatis, Kawashima, Werner: Quantum Monte Carlo Methods: algorithms for lattice models
Becca, Sorella : Quantum Monte Carlo approaches for correlated systems
Sandvik: "Computational Studies of quantum spin systems", arXiv:1101.3281
Schollwöck: "The density matrix renormalization group in the age of matrix product states", arXiv:1008.3477
Pollet: "Recent Developments in Quantum Monte Carlo simulations", arXiv:1206.0781
Lange, Van de Walle, Abedinnia, Bohrdt: "From architectures to applications: a reivew of neural quantum states", arXiv:2402.09402