Dependency graphs
Full graph
(9317 nodes)
Chapter 2 · Matrix Product Vectors
(62 nodes)
Chapter 3 · The Single-Block Fundamental Theorem
(20 nodes)
Chapter 4 · Perron–Frobenius Theory for Channels and Transfer Maps
(24 nodes)
Chapter 5 · Peripheral Channel Structure and Transfer-Operator Gaps
(50 nodes)
Chapter 6 · Wielandt Bound
(95 nodes)
Chapter 7 · Canonical Form Reduction
(124 nodes)
Chapter 8 · Basis of Normal Tensors
(142 nodes)
Chapter 9 · Proof of the Fundamental Theorem
(34 nodes)
Chapter 10 · Symmetries, Physical String Order, and Virtual-Boundary Nondecay
(436 nodes)
Chapter 11 · Parent-Hamiltonian Foundations: Injective and Normal Ground Spaces
(355 nodes)
Chapter 12 · Commuting Parent Hamiltonians and Spectral Gaps
(1001 nodes)
Chapter 13 · Block-Injective Parent Hamiltonians and Degenerate Ground Spaces
(223 nodes)
Chapter 14 · Exponential Decay of Correlations
(37 nodes)
Chapter 15 · Concrete Examples
(271 nodes)
Chapter 16 · Matrix Product Operators and Density Operators
(189 nodes)
Chapter 17 · Pure States: Renormalization of Matrix Product States
(139 nodes)
Chapter 18 · Matrix Product Unitaries
(919 nodes)
Chapter 19 · Finite-Group MPU Representations and Scalar Gauge Data
(463 nodes)
Chapter 20 · Mixed States: Renormalization of Matrix Product Operators
(870 nodes)
Chapter 21 · Mixed States: General Case and Algebraic Structure
(352 nodes)
Chapter 22 · Periodic MPS: irreducible form and the periodic Fundamental Theorem
(237 nodes)
Chapter 23 · The Algebraic Fundamental Theorem
(104 nodes)
Chapter 24 · Projected entangled pair states and the Fundamental Theorem
(526 nodes)
Chapter 25 · Examples of PEPS on the torus
(64 nodes)
Chapter 26 · G-injective PEPS and quantum double models
(727 nodes)
Chapter 27 · Ground spaces and reduced densities of PEPS regions
(1581 nodes)
Chapter 28 · Positive quasi-local constraints from a global gap
(262 nodes)
Chapter 29 · The Multi-Block Asymmetric Fundamental Theorem
(103 nodes)
Chapter 30 · Matrix Product Operator Symmetries and Non-Invertible Symmetries
(370 nodes)
Chapter 31 · Physics Examples of the Multi-Block Compression Theorem
(370 nodes)
Chapter 32 · Matrix Product Operator Algebras
(47 nodes)
Chapter 33 · Local Quantum Circuits
(134 nodes)
Chapter 34 · Sequential Generation of Matrix Product States
(71 nodes)
Chapter 35 · Preparation of Matrix Product States by Log-Depth Circuits
(380 nodes)
Chapter 36 · Interaction counting in lattice domains
(52 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
(62 nodes)
Chapter D · Canonical Form Reduction: Supporting Results
(76 nodes)
Chapter E · Basis of Normal Tensors: Supporting Results
(61 nodes)
Chapter F · Proof of the Fundamental Theorem: Supporting Results
(37 nodes)
Chapter G · Symmetries and Virtual-Boundary Nondecay: Supporting Results
(40 nodes)
Chapter H · Relative Commutants of Full Matrix Algebras: Supporting Results
(6 nodes)
Chapter I · Physics Examples of the Multi-Block Compression Theorem: Supporting Results
(26 nodes)
Fundamental-theorem gauge cone
(118 nodes)