dc.contributor.author
Cevolani, Lorenzo
dc.contributor.author
Carleo, Giuseppe
dc.contributor.author
Sanchez-Palencia, Laurent
dc.date.accessioned
2018-12-20T07:35:50Z
dc.date.available
2017-06-12T13:14:01Z
dc.date.available
2018-12-20T07:35:50Z
dc.date.issued
2016-09
dc.identifier.issn
1367-2630
dc.identifier.other
10.1088/1367-2630/18/9/093002
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/120960
dc.identifier.doi
10.3929/ethz-b-000120960
dc.description.abstract
We study the out-of-equilibrium dynamics induced by quantum quenches in quadratic Hamiltonians featuring both short- and long-range interactions. The spreading of correlations in the presence of algebraic decaying interactions, 1/R α , is studied for lattice Bose models in arbitrary dimension D. These models are exactly solvable and provide useful insight in the universal description of more complex systems as well as comparisons to the known universal upper bounds for the spreading of correlations. Using analytical calculations of the dominant terms and full numerical integration of all quasi-particle contributions, we identify three distinct dynamical regimes. For strong decay of interactions, $\alpha \gt D+1$, we find a causal regime, qualitatively similar to what previously found for short-range interactions. This regime is characterized by ballistic (linear cone) spreading of the correlations with a cone velocity equal to twice the maximum group velocity of the quasi-particles. For weak decay of interactions, α < D, we find instantaneous activation of correlations at arbitrary distance. This signals the breaking of causality, which can be associated with the divergence of the quasi-particle energy spectrum. Finite-size scaling of the activation time precisely confirms this interpretation. For intermediate decay of interactions, $D\lt \alpha \lt D+1$, we find a sub-ballistic, algebraic (bent cone) spreading and determine the corresponding exponent as a function of α. These outcomes generalize existing results for one-dimensional systems to arbitrary dimension. We precisely relate the three regimes to the first- and second-order divergences of the quasi-particle energy spectrum for any dimension. The long-range transverse Ising model in dimensions D = 1, 2, and 3 in the (quadratic) spin-wave approximation is more specifically studied and we also discuss the shape of the correlation front in dimension higher than one. Our results apply to several condensed-matter systems as well as atomic, molecular, and optical systems, and pave the way to the observation of causality and its breaking in diverse experimental realization.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Institute of Physics
en_US
dc.rights.uri
dc.title
Spreading of correlations in exactly solvable quantum models with long-range interactions in arbitrary dimensions
en_US
dc.type
Journal Article
ethz.journal.title
New Journal of Physics
ethz.journal.volume
18
en_US
ethz.journal.abbreviated
New j. phys.
ethz.pages.start
093002
en_US
ethz.size
18 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.identifier.nebis
001997538
ethz.publication.place
London
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2017-06-12T13:15:15Z
ethz.source
ECIT
ethz.identifier.importid
imp593654bd897d330021
ethz.ecitpid
pub:183043
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-12T11:33:40Z
ethz.rosetta.lastUpdated
2018-12-20T07:36:02Z
ethz.rosetta.versionExported
true
ethz.COinS