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Register a new userShielding Property in Higher Dimensions
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Nat\\'alia Salom\\'e M\\'oller
Publication date
2019
fields
Physics
and research's language is
English
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When the reduced state of a many-body quantum system is independent of its remaining parts, we say it shows what has become known by shielding property. Under some assumptions, equilibrium states of quantum transverse Ising models do manifest such phenomenon. Namely, imagine a many-body quantum system described by a lattice in the presence of an external magnetic field. Suppose there exists a separating interface on this lattice splitting the system into two subsets such that they only interact one another through that interface. In addition, suppose also that the applied external magnetic field is null on the interface. The shielding property states that the reduced state of the set in one side of the interface has no dependence on the Hamiltonian parameters of the set in the other side. This statement was proved in [N. Moller et al, PRE 97, 032101 (2018)] for the case where there is only one site in the interface. For lattices with more sites in the interface, it was conjectured that the shielding property is true when the system is in the ground state. For the case of positive temperatures, it does not hold and there are counterexamples to show that. Here we show that the conjecture does hold true for ground states, but under an additional condition. This condition is met, in particular, if the Hamiltonian terms associated to the interface are frustration-free.
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We show that Gibbs states of non-homogeneous transverse Ising chains satisfy a emph{shielding} property. Namely, whatever the fields on each spin and exchange couplings between neighboring spins are, if the field in one particular site is null, the reduced states of the subchains to the right and to the left of this site are emph{exactly} the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, we can guarantee a similar result only if the surface contains a single site. Already for an interface with two sites we show an example where the property does not hold. When it holds, however, we show that if a perturbation of the Hamiltonian parameters is done in one side of the lattice, the other side is completely unchanged, with regard to both its equilibrium state and dynamics.
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