Dependency graphs
Full graph
(3058 nodes)
Chapter 2 · Matrix Product Vectors
(51 nodes)
Chapter 3 · The Single-Block Fundamental Theorem
(16 nodes)
Chapter 4 · Transfer Maps and Quantum-Channel Interfaces
(11 nodes)
Chapter 5 · Perron–Frobenius Theory for Channels and Transfer Maps
(24 nodes)
Chapter 6 · Peripheral Channel Structure and Transfer-Operator Gaps
(50 nodes)
Chapter 7 · Wielandt Bound
(85 nodes)
Chapter 8 · Canonical Form Reduction
(119 nodes)
Chapter 9 · Basis of Normal Tensors
(139 nodes)
Chapter 10 · Proof of the Fundamental Theorem
(34 nodes)
Chapter 11 · Symmetries, Physical String Order, and Virtual-Boundary Nondecay
(78 nodes)
Chapter 12 · Parent-Hamiltonian Foundations: Injective and Normal Ground Spaces
(216 nodes)
Chapter 13 · Commuting Parent Hamiltonians and Spectral Gaps
(374 nodes)
Chapter 14 · Block-Injective Parent Hamiltonians and Degenerate Ground Spaces
(163 nodes)
Chapter 15 · Exponential Decay of Correlations
(18 nodes)
Chapter 16 · Concrete Examples
(92 nodes)
Chapter 17 · Matrix Product Operators and Density Operators
(171 nodes)
Chapter 18 · Pure States: Renormalization of Matrix Product States
(145 nodes)
Chapter 19 · Matrix Product Unitaries
(522 nodes)
Chapter 20 · Mixed States: Renormalization of Matrix Product Operators
(861 nodes)
Chapter 21 · Mixed States: General Case and Algebraic Structure
(301 nodes)
Chapter 22 · Periodic MPS: irreducible form and the periodic Fundamental Theorem
(133 nodes)
Chapter A · Perron–Frobenius Theory for Channels and Transfer Maps: Supporting Results
(2 nodes)
Chapter B · Peripheral Channel Structure and Transfer-Operator Gaps: Supporting Results
(18 nodes)
Chapter C · Wielandt Bound: Supporting Results
(61 nodes)
Chapter D · Canonical Form Reduction: Supporting Results
(72 nodes)
Chapter E · Basis of Normal Tensors: Supporting Results
(62 nodes)
Chapter F · Proof of the Fundamental Theorem: Supporting Results
(37 nodes)
Chapter G · Symmetries and Virtual-Boundary Nondecay: Supporting Results
(40 nodes)
Fundamental-theorem gauge cone
(115 nodes)