Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices

arXiv:2609.25276 · cond-mat.mes-hall, cond-mat.dis-nn, physics.comp-ph · Submitted 2026-09-21 · Read on arXiv

cond-mat.mes-hall, cond-mat.dis-nn, physics.comp-ph

Submitted: 2026-09-21

Updated: 2026-09-21

Terminology

• Hilbert Space — 8× in this paper · explained in 2 episodes
• Entanglement — 7× in this paper · explained in 3 episodes
• Generalization — 6× in this paper · explained in 13 episodes
• Chebyshev Polynomials — 4× in this paper · explained in 2 episodes
• Hubbard Model — 4× in this paper · explained in 3 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Matrix Product States (MPS) — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Control of single spin-flips in a Rydberg atomic fractal
• Compression, simulation, and synthesis of turbulent flows with tensor trains
• Tensor network solvers for ultra-large tight-binding Hamiltonians: algorithms and applications
• Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns

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