Quantum Dynamics   2VU    WS 2026/27

• Announcement of class:  pdf
  
  
• Notes:
  
  
• The use of Artificial Intelligence is encouraged (but not necessary).
  
  
• The class can naturally extend to a small research project in the Research Laboratory Advanced Computational Physics, PHT502,
  within the same module, which can be done at any time during the year.
  
  

• Time evolution of strongly correlated 1d systems by Matrix Product State ansatz:
  

• Lecture notes: pdf (with comments pdf)
  
  
• Main Exercise: Time evolution with MPS:  pdf
  
  Related notes: Presentation on bound states (H.G. Evertz, Montreal and Munich, 2015)  pdf
  
  
• Exercise: increase of entanglement with time:   S ~ t generically  (S~log t  in special cases):
  M. Gruber, Masters Thesis, 2017 pdf  (exercise on page 29; examples for S(t) on pages 37 and 41)
  Review on Entanglement, L. Amico et al, Rev. Mod. Phys 18, 517-576 (2008)  pdf  (see pages 566, 567, "Dynamics of the block entropy")
  
  

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• Additional information on MPS  (not required)
  
  
• Detailed background on MPS (Matrix Product States) and on Time evolution:
  

  Review by U. Schollwöck in Advances in Physics, 2011 pdf
  Masters thesis, Lukas Grabenwarter 2020 pdf
  Masters thesis, Valentin Zauner 2011 pdf
  Diploma thesis, Elias Rabel 2010 pdf        
  

• 2x2 A-matrices and Gamma-Lambda matrices for a single-particle state (e.g. Gaussian): pdf from chat
  
  
• Additional information on reduced density matrix etc. (from Course on Quantum Mechanics, mostly translated into English:)
• QM_chap9_density_matrix   QM_app_A14_derivation    QM_chap10_entangled_states
  
  
• Additional information on bound states:
  

            Introduction to the Bethe Ansatz, Karbach & Müller 1998  pdf I  pdf II
            Diploma thesis, Martin Ganahl 2010  pdf 

            Bachelors thesis, Michael Scherbela 2014  pdf

            Publication:  Martin Ganahl, Elias Rabel, Fabian H. L. Essler, and H. G. Evertz
                                            Observation of Complex Bound States in the Spin-1/2 Heisenberg XXZ Chain Using Local Quantum Quenches
                                            Phys. Rev. Lett. 108, 077206 (2012) pdf

• Further information:
  

  Lecture notes on Heisenberg-Model with ground state calculation by Exact Diagonalization (Lanczos method, similar to, Conjugate Gradients)
  
  

• Full diagonalization: instructions and exercise:  pdf  (more explanations in lecture 2022-12-19, online in TeachCenter)
  
  

• Additional information presented in class:
  
  

• Obtaining spectra with MPS time evolution

• Old standard: Quantum Monte Carlo simulations in imaginary time.
  Examples: H. Endres, Dissertation 1d-QMC Hubbard, 1996 pdf,   C. Dahnken, Diplomarbeit 2d-QMC Hubbard, 1995 pdf
  
  
• Much more precise spectra from MPS time evolution, including 'linear extrapolation':
  Example: G. Winkler, Master Thesis, MPS, spin orbit coupled chains, 2014: talk, thesis
  
  

• Application of MPS to modelling of real materials:
  Talk on DMFT impurity solver with Fork Tensor Product States (MPS) (HGE, Jülich Autumn school 2018) pdf
  
  

• Application of many body time evolution: Photon excitation of strongly correlated electrons (solar cells):
  Talk on Hubbard model plus light pulse, "Impact Ionization" (Florian Maislinger, 2018)  pdf
  
  

• Talk on Quantum Simulators with Cold Neutral Atoms:
  I. Bloch, public lecture at the KITP, Santa Barbara, 2016  pdf     (more technical details: pdf)
  
  

• Tutorial on Quantum Simulation, Complexity, and Quantum Information:
  I. Deutsch, Qsim tutorial at APS March Meeting 2011  pdf
  
  

• Quantum Simulation of the 1d Hubbard model up to 700 hopping times:
  Madhusudhana et al. PRX Quantum 2, 040325 (2021)   pdf