Parametrized isometric tensor networks called skeletons deform abelian string-net fixed points via symmetry conservation and isometry constraints, connecting topological phases through critical points and enabling efficient classical computation of generalized Pauli string expectations.
PEPS as unique ground states of local Hamiltonians
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abstract
In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region. While it implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.
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quant-ph 1years
2025 1verdicts
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Skeleton of isometric Tensor Network States for Abelian String-Net Models
Parametrized isometric tensor networks called skeletons deform abelian string-net fixed points via symmetry conservation and isometry constraints, connecting topological phases through critical points and enabling efficient classical computation of generalized Pauli string expectations.