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Time-evolution of local information: thermalization dynamics of local observables
by Thomas Klein Kvorning, Loïc Herviou, Jens H. Bardarson
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Submission summary
| Authors (as registered SciPost users): | Jens H Bardarson · Thomas Klein Kvorning |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2105.11206v4 (pdf) |
| Date accepted: | 2022-08-22 |
| Date submitted: | 2022-08-18 07:57 |
| Submitted by: | Klein Kvorning, Thomas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Quantum many-body dynamics generically results 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 decoupling 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 can motivate algorithms based on the intuition that information for statistical reasons flow 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.
Author comments upon resubmission
Thank you for your patience and time spent on our manuscript. We have now updated the manuscript to include the discussion with the second referee.
The main content in discussion with the referee not in the earlier manuscripts is the discussion on the N-representability problem. We previously omitted such a discussion since we thought it would distract attention from the article's main points. However, after the conversation with the referee, it was clear that it could be beneficial to discuss the subject. We added a paragraph in section 5, which includes the content from the discussion with the referee.
A related issue in the discussion is controlling the error in our algorithm. To make that more transparent, we rewrote parts of sections 4 and 5 to emphasize that we have a small controlled bound on the error under certain circumstances, and otherwise, we only control the error by convergence with the truncation variable.
One part of this discussion discussed the scope and aim of the article, which the referee initially misunderstood. This was already made significantly more pedagogical with the rewriting of our introduction after the first referee round, and the misunderstandings brought into the second round would not have occurred if the referee had read the new version first. Therefore we have not added any further discussion of this in the introduction.
With these changes, we hope the article will be accepted for publication in SciPost Physics.
Published as SciPost Phys. 13, 080 (2022)