Holographic State Complexity from Group Cohomology

Bartłomiej Czech ()
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Bartłomiej Czech: Tsinghua University, Institute for Advanced Study

A chapter in Nankai Symposium on Mathematical Dialogues, 2026, pp 129-138 from Springer

Abstract: Abstract Topological phases of matter are often described using auxiliary systems in one extra dimension. I review the one-dimensional cluster state—the simplest quantum state with Symmetry-Protected Topological (SPT) order—as a toy model of holographic duality, and inspect it for clues about defining holographic complexity. Group cohomology, which classifies SPT orders, is a viable candidate for a robust definition of complexity in gauge/gravity duality.

Date: 2026
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DOI: 10.1007/978-981-19-2328-9_14

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