Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
arXiv (Cornell University)(2023)
摘要
The study of frustration-free Hamiltonians and their relation to finite
bond-dimension matrix product states (MPS) has a long tradition. However,
fractional quantum Hall (FQH) states do not quite fit into this theme since the
known MPS representations of their ground states have infinite bond dimensions,
which considerably obscures the relations between such MPS representations and
the existence of frustration-free parent Hamiltonians. This is related to the
fact that the latter necessarily are of infinite range in the orbital basis.
Here, we present a theorem tailored to establishing the existence of
frustration-free parent Hamiltonians in such a context. We explicitly
demonstrate the utility of this theorem in the context of non-Abelian
Moore-Read FQH states but argue the applicability of this theorem to transcend
considerably beyond the realm of conformal-field-theory-derived MPSs or
quasi-one-dimensional Hilbert spaces.
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关键词
bond-dimension,frustration-free
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