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Time-evolution of local information: Thermalization dynamics of local observables
KTH, School of Engineering Sciences (SCI), Physics. Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA..ORCID iD: 0000-0001-7399-9618
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory. Ecole Polytech Fed Lausanne EPFL, Inst Phys, CH-1015 Lausanne, Switzerland..ORCID iD: 0000-0003-4220-8785
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-3328-8525
2022 (English)In: SciPost Physics, E-ISSN 2542-4653, Vol. 13, no 4, article id 080Article in journal (Refereed) Published
Abstract [en]

Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well-defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time-evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such de-coupling of local degrees of freedom for the mixed-field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we motivate algorithms based on the intuition that information for statistical reasons flows from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed-field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

Place, publisher, year, edition, pages
Stichting SciPost , 2022. Vol. 13, no 4, article id 080
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-321274DOI: 10.21468/SciPostPhys.13.4.080ISI: 000869464500008Scopus ID: 2-s2.0-85142368062OAI: oai:DiVA.org:kth-321274DiVA, id: diva2:1710112
Note

QC 20221111

Available from: 2022-11-11 Created: 2022-11-11 Last updated: 2023-06-08Bibliographically approved

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Klein Kvorning, ThomasHerviou, LoicBardarson, Jens H.

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