6533b872fe1ef96bd12d3885
RESEARCH PRODUCT
Mutual information and spontaneous symmetry breaking
Alioscia HammaSalvatore Marco GiampaoloFabrizio Illuminatisubject
PhysicsQuantum discordQuantum PhysicsStrongly Correlated Electrons (cond-mat.str-el)FOS: Physical sciencesQuantum capacityQuantum entanglementCoherent information01 natural sciencesQuantum relative entropyAtomic and Molecular Physics and Optics010305 fluids & plasmasCondensed Matter - Strongly Correlated ElectronsQuantum mechanicsAtomic and Molecular Physics0103 physical sciencesand Optics010306 general physicsQuantum mutual informationAmplitude damping channelmutual informationQuantum Physics (quant-ph)Joint quantum entropydescription
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual information based on the $2-$R\'enyi entanglement entropy and using a locality result stemming from quasi-adiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum $XY$ model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-27 |