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Integrability of open boundary driven quantum circuits
by Chiara Paletta, Tomaž Prosen
Submission summary
Authors (as registered SciPost users): | Chiara Paletta |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2406.12695v2 (pdf) |
Date submitted: | 2024-07-19 18:17 |
Submitted by: | Paletta, Chiara |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
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Approach: | Theoretical |
Abstract
In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate the cases where the bulk is given by elementary six vertex unitary gates of either the free fermionic XX type or interacting XXZ type. By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet (aka brickwork) dynamics. We prove that, only if the bulk is a free-model, the boundary matrices are in general non-factorizable, and for particular choice of free parameters yield non-trivial unitary dynamics with boundary interaction between the two chains. Then, we consider the limit of continuous time evolution and we give the interpretation of a restricted set of the boundary terms in the Lindbladian setting. Specifically, for a particular choice of free parameters, the solutions correspond to an open quantum system dynamics with the source terms representing injecting or removing particles from the boundary of the spin chain.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block