Integrable spin chains and the Clifford group
- URL: http://arxiv.org/abs/2107.02184v2
- Date: Fri, 8 Apr 2022 08:35:04 GMT
- Title: Integrable spin chains and the Clifford group
- Authors: Nick G. Jones and Noah Linden
- Abstract summary: We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant.
For spin chains solvable by algebraic Bethe Ansatz, we explain how conjugating by a matrix product operator affects the underlying integrable structure.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We construct new families of spin chain Hamiltonians that are local,
integrable and translationally invariant. To do so, we make use of the Clifford
group that arises in quantum information theory. We consider translation
invariant Clifford group transformations that can be described by matrix
product operators (MPOs). We classify the translation invariant Clifford group
transformations that consist of a shift operator and an MPO of bond dimension
two -- this includes transformations that preserve locality of all
Hamiltonians; as well as those that lead to non-local images of particular
operators but nevertheless preserve locality of certain Hamiltonians. We
characterise the translation invariant Clifford group transformations that take
single-site Pauli operators to local operators on at most five sites --
examples of Quantum Cellular Automata -- leading to a discrete family of
Hamiltonians that are equivalent to the canonical XXZ model under such
transformations. For spin chains solvable by algebraic Bethe Ansatz, we explain
how conjugating by a matrix product operator affects the underlying integrable
structure. This allows us to relate our results to the usual classifications of
integrable Hamiltonians. We also treat the case of spin chains solvable by free
fermions.
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