Local factorisation of the dynamics of quantum spin systems

Sven Bachmann; Andreas Bluhm

doi:10.1063/1.4991949

Local factorisation of the dynamics of quantum spin systems

Sven Bachmann, Andreas Bluhm

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

Motivated by the study of area laws for the entanglement entropy of gapped ground states of quantum spin systems and their stability, we prove that the unitary cocycle generated by a local time-dependent Hamiltonian can be approximated, for any finite set X, by a tensor product of the corresponding unitaries in X and its complement, multiplied by a dynamics strictly supported in the neighbourhood of the surface ∂X. The error decays almost exponentially in the size of the neighbourhood and grows with the square of the area |∂X|².

Original language	English
Journal	Journal of Mathematical Physics
Volume	58
Issue number	7
ISSN	0022-2488
DOIs	https://doi.org/10.1063/1.4991949
Publication status	Published - 1 Jul 2017

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abstract = "Motivated by the study of area laws for the entanglement entropy of gapped ground states of quantum spin systems and their stability, we prove that the unitary cocycle generated by a local time-dependent Hamiltonian can be approximated, for any finite set X, by a tensor product of the corresponding unitaries in X and its complement, multiplied by a dynamics strictly supported in the neighbourhood of the surface ∂X. The error decays almost exponentially in the size of the neighbourhood and grows with the square of the area |∂X|2.",

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N2 - Motivated by the study of area laws for the entanglement entropy of gapped ground states of quantum spin systems and their stability, we prove that the unitary cocycle generated by a local time-dependent Hamiltonian can be approximated, for any finite set X, by a tensor product of the corresponding unitaries in X and its complement, multiplied by a dynamics strictly supported in the neighbourhood of the surface ∂X. The error decays almost exponentially in the size of the neighbourhood and grows with the square of the area |∂X|2.

AB - Motivated by the study of area laws for the entanglement entropy of gapped ground states of quantum spin systems and their stability, we prove that the unitary cocycle generated by a local time-dependent Hamiltonian can be approximated, for any finite set X, by a tensor product of the corresponding unitaries in X and its complement, multiplied by a dynamics strictly supported in the neighbourhood of the surface ∂X. The error decays almost exponentially in the size of the neighbourhood and grows with the square of the area |∂X|2.

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M3 - Journal article

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VL - 58

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

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Local factorisation of the dynamics of quantum spin systems

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