Local factorisation of the dynamics of quantum spin systems

TY - JOUR

T1 - Local factorisation of the dynamics of quantum spin systems

AU - Bachmann, Sven

AU - Bluhm, Andreas

PY - 2017/7/1

Y1 - 2017/7/1

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.

UR - http://www.mendeley.com/research/local-factorisation-dynamics-quantum-spin-systems

U2 - 10.1063/1.4991949

DO - 10.1063/1.4991949

M3 - Journal article

SN - 0022-2488

VL - 58

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 7

ER -