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PEPS as ground states: degeneracy and topology

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arxiv 1001.3807 v3 pith:3R2TKY34 submitted 2010-01-21 quant-ph cond-mat.str-el

PEPS as ground states: degeneracy and topology

Norbert Schuch , Ignacio Cirac , David Perez-Garcia This is my paper
classification quant-ph cond-mat.str-el
keywords statesgroundpepssymmetriesframeworktopologicalactingallows
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Renormalization flows for 1D mixed states and a quantum Goursat lemma

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    Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.

  2. Exact Quantum Many-Body Scars by a generalized Matrix-Product Ansatz

    quant-ph 2026-05 unverdicted novelty 7.0

    Exact eigenstates of non-frustration-free quantum many-body systems are constructed via a local error cancellation matrix-product ansatz.

  3. Exact Quantum Many-Body Scars by a generalized Matrix-Product Ansatz

    quant-ph 2026-05 conditional novelty 6.0

    An error-cancellation matrix-product ansatz constructs exact zero-energy many-body scar eigenstates in non-frustration-free 1D and 2D spin Hamiltonians.

  4. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.