[AI English Translation of Notes]

This page lists AI-assisted English translations of selected Japanese notes. The original Japanese page is here.

[Lecture Notes and Expository Articles]

1. Intensive Lectures on Matrix Product States pdf (existing translation) original Japanese pdf

[Notes]

1. Notes on Bloch Hamiltonians and Berry Phases pdf (AI translation) original Japanese pdf
2. Note: The Bethe Ansatz pdf (AI translation) original Japanese pdf
3. Matrix Product State pdf (AI translation) original Japanese pdf
4. Note: On Lattice Approximation Formulae for Topological Invariants pdf (AI translation) original Japanese pdf
5. Note: Area Law for One-Dimensional Frustration-Free Systems pdf (AI translation) original Japanese pdf

[Personal Memos]

• Space Groups, Representation Theory, and K-Theory
1. On Chiral Indices and Winding Numbers pdf (AI translation) original Japanese pdf
2. On the Computation of Fundamental Domains pdf (AI translation) original Japanese pdf
3. On Space-Group-Symmetric Cell Decompositions of Real Space and Momentum Space pdf (AI translation) original Japanese pdf
4. On the Degree of K-Groups, Symmetry Groups, and Factor Systems pdf (AI translation) original Japanese pdf
5. On induced representations and irreducible decompositions pdf (AI translation) original Japanese pdf
6. A Note on the Definition of the Relative K-Group pdf (AI translation) original Japanese pdf
7. Notes on Factor Systems in Momentum Space pdf (AI translation) original Japanese pdf
8. Coset Decomposition of a Finite Group pdf (AI translation) original Japanese pdf
9. Memo: Spin Space Groups pdf (AI translation) original Japanese pdf
• Topological Insulators and Superconductors: Condensed-Matter Notes
1. Note: Bound-State Solutions of a One-Dimensional Dirac Hamiltonian pdf (AI translation) original Japanese pdf
2. Irreducible Decomposition of a Superconducting Gap Function pdf (AI translation) original Japanese pdf
3. Class D and Symmetry in Fermionic Many-Body Systems pdf (AI translation) original Japanese pdf
4. Computing Homotopy Classes of Loops in SO(n) pdf (AI translation) original Japanese pdf
5. Fermi-Surface Formula for Topological Invariants in Superconductors pdf (AI translation) original Japanese pdf
6. Memo: A Direct Proof of Quantization of Z Topological Invariants pdf (AI translation) original Japanese pdf
7. Note: Zero modes at disclination defects in $C_4$-symmetric superconductors pdf (AI translation) original Japanese pdf
8. PT Symmetry and Topological Invariants (Draft) pdf (AI translation) original Japanese pdf
9. Computing the Berry Phase on a Fermi Loop by a Lattice Approximation pdf (AI translation) original Japanese pdf
10. On the Kane--Mele Z2 Invariant pdf (AI translation) original Japanese pdf
11. On Obstructions to Exponentially Localized Wannier States pdf (AI translation) original Japanese pdf
12. Some properties of class-D Hamiltonians pdf (AI translation) original Japanese pdf
13. Note: Winding Numbers (Draft) pdf (AI translation) original Japanese pdf
14. Inversion Symmetry and Wannier States pdf (AI translation) original Japanese pdf
15. Canonical Adiabatic Pump: 1D Class D pdf (AI translation) original Japanese pdf
16. A Lattice Approximation to the Winding Number and the WZW Term pdf (AI translation) original Japanese pdf
17. A Calculation Note on the Chern--Simons 3-Form pdf (AI translation) original Japanese pdf
18. A memo on the construction of the $\pi_n[R_{2-n}]=\Z_2$ invariant pdf (AI translation) original Japanese pdf
19. On $c_1(E)\equiv w_2(E_R)$ pdf (AI translation) original Japanese pdf
20. Berry Connection pdf (AI translation) original Japanese pdf
21. A Note on Delicate Insulators Protected by Crystalline Symmetry pdf (AI translation) original Japanese pdf
22. Memo: Wannier States and Spectral Flow pdf (AI translation) original Japanese pdf
23. A Note on Redefining the Second Stiefel--Whitney Class pdf (AI translation) original Japanese pdf
24. On the Gauge Invariance of c1 and w2 pdf (AI translation) original Japanese pdf
25. A Gauged Expression for the Three-Dimensional Winding Number pdf (AI translation) original Japanese pdf
26. On the Construction of a Real Berry Connection in Band Theory pdf (AI translation) original Japanese pdf
27. Computation of the Chern-Number Density in a Dirac Model pdf (AI translation) original Japanese pdf
28. A Note on the Unit-Cell-Center Dependence of the Chern--Simons Term pdf (AI translation) original Japanese pdf
• Non-Hermitian Systems
1. Line Gaps and Hermitianization pdf (AI translation) original Japanese pdf
2. On $\lim_{N \to \infty} {\rm sp}(V_{\rm OBC}) \subset {\rm sp}(V_{\rm SIBC})$ pdf (AI translation) original Japanese pdf
3. Derivation of the 54 and 38 Symmetry Classes for Non-Hermitian Hamiltonians pdf (AI translation) original Japanese pdf
4. Memo: Symmetry in Non-Hermitian Systems pdf (AI translation) original Japanese pdf
5. Compatibility of Flattening with Symmetry for Point-Gapped Hamiltonians pdf (AI translation) original Japanese pdf
• Invertible Phases
1. Note: Two-Parameter Pumps pdf (AI translation) original Japanese pdf
2. Notes on the Chen--Gu--Liu--Wen Cocycle Model pdf (AI translation) original Japanese pdf
3. Computation memo: Does the Chen--Gu--Liu--Wen cocycle model agree with the Levin--Gu model? pdf (AI translation) original Japanese pdf
4. MPS and Symmetry: A Calculation Note pdf (AI translation) original Japanese pdf
5. Local Unitary Symmetry Actions and H^3(G,U(1)) pdf (AI translation) original Japanese pdf
6. Note: On Wall's Structure Theorem pdf (AI translation) original Japanese pdf
7. Chain Complexes, Cochain Complexes, and Descent Equations pdf (AI translation) original Japanese pdf
8. The Cech--de Rham Complex pdf (AI translation) original Japanese pdf
9. Adiabatic Pumps and Berry Phases in One-Dimensional Spin Systems with Z2 Symmetry pdf (AI translation) original Japanese pdf
10. Ground States of the Kitaev Chain pdf (AI translation) original Japanese pdf
11. On the Behavior of Transfer Matrices between MPS pdf (AI translation) original Japanese pdf
12. Spin-Chain Models on $RP^2x S^1$ and $L(3,1)x S^1$ pdf (AI translation) original Japanese pdf
13. Memo: Higher Berry Curvature and Lattice Models pdf (AI translation) original Japanese pdf
14. A Theorem on Reductions of MPS pdf (AI translation) original Japanese pdf
• Quantum Many-Body Systems
1. Detectability Lemma pdf (AI translation) original Japanese pdf
2. Representing a Ground State of a Hamiltonian by Constraints from Local Terms pdf (AI translation) original Japanese pdf
3. Approximation Accuracy of MPS and Renyi Entropy pdf (AI translation) original Japanese pdf
4. A Calculation Note on the LSM Theorem pdf (AI translation) original Japanese pdf
5. Note: Knabe's Method pdf (AI translation) original Japanese pdf
• Linear Algebra, Matrices, and Group Theory
1. The Pseudoinverse Matrix pdf (AI translation) original Japanese pdf
2. On Computing Homomorphisms of Z-Modules pdf (AI translation) original Japanese pdf
3. The Baer Sum pdf (AI translation) original Japanese pdf
4. The Min-Max Theorem pdf (AI translation) original Japanese pdf
5. Weyl's Inequality pdf (AI translation) original Japanese pdf
6. The Eckart--Young--Mirsky Theorem pdf (AI translation) original Japanese pdf
7. Contractivity of the Trace Norm pdf (AI translation) original Japanese pdf
8. Goursat's Lemma pdf (AI translation) original Japanese pdf
• Miscellaneous
1. Note: Stark Localization pdf (AI translation) original Japanese pdf
2. Imaginary-Time Evolution and the Berry Phase pdf (AI translation) original Japanese pdf
3. Overlap Integrals of Fermionic Wave Functions pdf (AI translation) original Japanese pdf
4. Derivation of Wick's theorem and the Schwinger term pdf (AI translation) original Japanese pdf
5. The Gawedzki--Reis Construction of the WZ Term pdf (AI translation) original Japanese pdf
6. Axioms for Spectral Sequences (Draft) pdf (AI translation) original Japanese pdf
7. The Polyakov--Wiegmann Formula for Non-Simply-Connected Groups pdf (AI translation) original Japanese pdf
8. Relation Between the Wess--Zumino Term and the Chern--Simons Term pdf (AI translation) original Japanese pdf
9. On Local Formulae for Stiefel--Whitney Classes pdf (AI translation) original Japanese pdf
10. $C^*$-Geometric Phase: Viennot--Lages Formalism (Draft) pdf (AI translation) original Japanese pdf
• Topology
1. The Barycentric Subdivision Operator pdf (AI translation) original Japanese pdf
2. Notes: Cubical Singular Chain Complexes pdf (AI translation) original Japanese pdf
3. Memo: Universal Connections pdf (AI translation) original Japanese pdf
4. Reading Cheeger--Simons pdf (AI translation) original Japanese pdf
5. The Cohomology Rings of BSO and BO pdf (AI translation) original Japanese pdf
6. Memo: On Stable Framed Cobordism pdf (AI translation) original Japanese pdf
• Project Notes
1. Classification of Surface States of Topological Insulators and Superconductors pdf (AI translation) original Japanese pdf
2. Memo pdf (AI translation) original Japanese pdf
3. Notes on {Topological terms of (2+1)d flag-manifold sigma models} pdf (AI translation) original Japanese pdf
4. Entanglement entropy of fermions pdf (AI translation) original Japanese pdf