Inhaltsbereich
Tensor Networks – Lecture notes
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Lecture Notes:
Lecture Notes:
| Lecture | Date | Notes | Pages | Topic |
| T14 | 25.07.19 | Tutorial:MPS-based machine learning | ||
| L23 | 24.07.19 | ML.1 ML.2 | Machine learning 1. Neural networks 2. Supervised learning with tensor networks | |
| L22 | 22.07.19 | F-PEPS.1 F-PEPS.2 F-PEPS.3 F-PEPS.4 | Fermionic PEPS 1. Parity conservation 2. Fermionic signs 3. Jump move 4. Examples | |
| T13 | 18.07.19 | Tutorial: GILT, FET | ||
| L21 | 17.07.19 | CanF.1 CanF.2 CanF.3 | 2D Canonical Forms, Isometric PEPS 1. Canonical form for bond in 2D tensor network 2. Full environment truncation 3. Isometric PEPS | |
| L20 | 15.07.19 | TNR.1 TNR.2 TNR.3 TNR.4 TNR.5 TNR.6 | TNR: Tensor network renormalization 1. Motivation 2. TNR idea 3. Projective truncation 4. TNR details 5. TNR results in MERA 6. TNR benchmark results | |
| T12 | 11.07.19 | Tutorial: TRG, simple update | ||
| L19 | 10.07.19 | TRG-II.1 TRG-II.2 TRG-II.3 TRG-II.4 TRG-II.5 TRG-II.6 |
TRG-II: Graph-independent local truncations (Gilt) 1. Motivation 2. Why is TRG insufficient? 3. Environment spectrum 4. Gilt: Graph-independent local truncations 5. Gilt-TNR 6. Benchmark results |
|
| L18 | 08.07.19 | TRG-I.1 TRG-I.2 TRG-I.3 TRG-I.4 |
Tensor renormalization group (TRG) 1. TRG for 2D classical lattice models 2. TRG for quantum lattice models 3. Second renormalization (SRG) of tensor network states 4. Core tensor renormalization group (CTRG) |
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| T11 | 04.07.19 | Tutorial: PEPS I - exact contraction on a strip | ||
| L17 | 03.07.19 | PEPS-II.1 PEPS-II.2 | PEPS II: contractions via MPS techniques 1. PEPS via finite-size MPS 2. Infinite-size PEPS (iPEPS) | |
| L16 | 01.07.19 | PEPS-I.1 PEPS-I.2 PEPS-I.3 PEPS-I.4 |
PEPS I: Projected entangled-pair states 1. Motivation and Definition 2. Example: RVB state 3. Example: Kitaev's Toric Code 4. Example: Resonating AKLT state | |
| T10 | 27.06.19 | Tutorial: Symmetries & QSpace (continued) | ||
| T09 | 26.06.19 | Tutorial: Symmetries & QSpace | ||
| L15 | 24.06.19 | Sym-II.1 Sym-II.2 Sym-II.3 Sym-II.4 Sym-II.5 Sym-II.6 |
Symmetries II: Non-Abelian. 1. Motivation, SU(2) basics 2. Tensor product decomposition 3. Tensor operators 4. Example: direct product of two spin 1/2's 5. Example: direct product of three spin 1/2's 6. Bookkeeping for unit matrices | |
| 20.06.19 | Corpus Christi | |||
| L14 | 19.06.19 | Sym-I.1 Sym-I.1 Sym-I.1 |
Symmetries I: Abelian 1. Example: spin 1/2 XXZ-chain 2. Iterative diagonalization 3. QSpace bookkeeping for unit matrices | |
| T08 | 17.06.19 | Tutorial: tDMRG, purification, tangent space methods | ||
| L13 | 13.06.19 | TS.1 TS.2 TS.3 |
Tangent space methods 1. MPS and canonical forms. 2. Tangent space. 3. Tangent space projector. 4. Time evolution. |
|
| L12 | 12.06.19 | DMRG-II.1 DMRG-II.2 DMRG-II.3 |
DMRG II 1. Relation to traditional DMRG. 2. tDMRG. 3. Finite temperature: purification. |
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| 10.06.19 | Pentecost Monday | |||
| T07 | 06.06.19 | Tutorial: iTEBD | ||
| L11 | 05.06.19 | pdf |
MPS-V.1 iTEBD.1 iTEBD.2 iTEBD.3 iTEBD.4 |
MPS V: Vidal's Gamma-Lambda notation iTEBD: Infinite Time-Evolving Block Decimation 1. Basic iTEBD algorithm 2. iTEBD in Gamma-Lambda notation 3. iTEBD: Hastings' method 4. Orthogonalization |
| T06 | 03.06.19 | Tutorial: DMRG | ||
| 30.05.19 | Ascension Day | L10 | 29.06.19 | DMRG-I.1 DMRG-I.2 DMRG-I.3 DMRG-I.4 |
DMRG I: Density Matrix Renormalization Group - ground state search 1. Single-site optimization 2. Lancos Method 3. Excited states 4. Two-site optimization |
| L09 | 27.05.19 | MPS-IV.1 MPS-IV.2 MPS-IV.3 |
MPS IV: Matrix product operators 1. Applying MPO to MPS yields MPS 2. MPO representation of Heisenberg Hamiltonian 3. Applying MPO to mixed-canonical state |
|
| T05 | 23.05.19 | Tutorial: AKLT Model | L08 | 22.05.19 | AKLT.1 AKLT.2 AKLT.3 AKLT.4 AKLT.5 |
AKLT Model 1. General remarks 2. Construction of AKLT Hamiltonian 3. AKLT ground state 4. Transfer operator 5. String order parameter |
| L07 | 20.05.19 | MPS-III.1 MPS-III.2 MPS-III.3 |
MPS III: Translationally invariant MPS 1. Transfer matrix 2. Eigenvalues of transfer matrix 3. Correlation functions |
|
| T04 | 16.05.19 | Tutorial: NRG II/III | ||
| L06 | 20.05.19 6:15 | The notes for the entire lecture 06 have been thoroughly
revised. Please discard previous version and use this one. |
||
| L06 | 15.05.19 | NRG-III.1 NRG-III.2 NRG-III.3 NRG-III.4 NRG-III.5 NRG-III.6 NRG-III.7 |
NRG III: Thermal and dynamical quantities 1. Thermodynamic observables 2. Lehmann representation of spectral functions 3. Single-shell and patching schemes 4. Graphical notation for basis change 5. MPS notation for discarded/kept states 6. Complete many-body basis 7. Full density matrix NRG (fdmNRG) |
|
| L05 | 13.05.19 | NRG-II.1 NRG-II.2 NRG-II.3 NRG-II.4 NRG-II.5 NRG-II.6 NRG-II.7 |
Numerical Renormalization group (NRG) II: RG flow 1. Kondo model: low-order perturbation theory 2. Kondo model: poor man's scaling 3. General RG concepts 4. NRG iteration scheme from RG perspective 5. Uncoupled bath Hamiltonian: fixed points 6. Kondo model: fixed points and RG flow 7. Anderson model: fixed points and RG flow |
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| T03 | 09.05.19 | Tutorial: NRG I | L04 | 08.05.19 | NRG-I.1 NRG-I.2 NRG-I.3 NRG-I.4 |
NRG I: Numerical Renormalization group - Wilson chain 1. Single-impurity Anderson model 2. Logarithmic discretization 3. Wilson chain 4. Iterative diagonalization |
| L03 | 06.05.19 | MPS-II.1 MPS-II.2 MPS-II.3 |
MPS II: Diagonalization, fermionic signs 1. Iterative diagonalization of short spin chain 2. Spinless fermions 3. Spinful fermions |
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| T02 | 02.05.19 | Tutorial: MPS I | ||
| L02 | 02.05.19 9:10 | In Section 3, the discussion of operator matrix elements has been revised.
In section 4, handwritten text has been converted to typed text. |
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| 01.05.19 | Labor day | |||
| L02 | 29.04.19 | MPS-I.1 MPS-I.2 MPS-I.3 MPS-I.4 |
MPS 1: Matrix Product States 1. Overlap and normalization. 2. Canonical MPS forms (left, right, site, bond) 3. Matrix elements, expectation values 4. Schmidt decomposition |
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| L01 | 30.04.19 12:38 | In Section 3, Eqs. (12), (27) and (28), the order of the lower indices of A-dagger has been
reversed. |
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| L01 | 23.04.19 23:27 | In Sections 1 to 4, important notational changes were made regarding the definition
of tensor product spaces. |
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| T01 | 25.04.19 | Tutorial: MATLAB basics | L01 | 24.04.19 | TNB1 TNB2 TNB3 TNB4 TNB5 TNB6 |
Tensor Network basics (TNB): 1. Why study tensor networks? 2. Iterative diagonalization 3. Covariant index notation 4. Entanglement entropy and area laws 5. Tensor network diagrams 6. Singular-value decomposition (SVD) |
22.04.19 | Easter Monday |