Geometry of reduced density matrices for symmetry-protected topological phases

Abstract

In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low dimension projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system---no ruled surface emerges in systems without boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite system calculation suffices to reveal the ruled surface structures.

8 pages, 7 figures. Close to published version

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• Matrix product states represent ground states faithfully
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Cited by in corpus (10)

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• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Observing geometry of quantum states in a three-level system
• Symmetry Breaking and Convex Set Phase Diagrams for the q-state Potts Model
• Symmetry Breaking and the Geometry of Reduced Density Matrices
• Computing partial traces and reduced density matrices
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Physical origins of ruled surfaces on the reduced density matrices geometry
• A new signature of quantum phase transitions from the numerical range
• Quantum Phase Transitions in a Model Hamiltonian Exhibiting Entangled Simultaneous Fermion-Pair and Exciton Condensations