Schwinger-Keldysh nonperturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models

• URL: http://arxiv.org/abs/2405.00765v4
• Date: Fri, 28 Feb 2025 18:36:00 GMT
• Title: Schwinger-Keldysh nonperturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Authors: Felipe Reyes-Osorio, Federico Garcia-Gaitan, David J. Strachan, Petr Plechac, Stephen R. Clark, Branislav K. Nikolic,
• Abstract summary: We build a field-theoretic framework to handle many mutually interacting quantum spins of arbitrary value S.<n>Our framework tracks numerically exact benchmarks for spin-boson in the non-Markovian regime.<n>It is a promising route for simulation of driven-dissipative systems in quantum computing or quantum magnonics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Open quantum systems with many interacting degrees of freedom pose a formidable challenge for presently available theoretical methods, especially when dissipative environment imposes non-Markovian dynamics on them with memory effects and revival of genuine quantum properties. Even the archetypical spin-boson model, where a single spin-1/2 interacts with an infinite bosonic bath, requires switching between methods for different choice of system and bath parameters. Here, we construct a field-theoretic framework as a single methodology that can handle many mutually interacting quantum spins of arbitrary value S, spatial dimensionality, system-bath coupling, bath temperature and spectral properties of the bath. Our framework combines Schwinger-Keldysh field theory (SKFT) with two-particle irreducible (2PI) action resumming a class of Feynman diagrams to an infinite order originating from 1/N expansion, where N is the number of Schwinger bosons to which the spin is mapped. Remarkably, the SKFT+2PI approach closely tracks numerically exact benchmarks for spin-boson in the non-Markovian regime obtained from hierarchical equations of motion or tensor network methods. Furthermore, we demonstrate the ability of our SKFT+2PI framework to compute two-spin correlators of an antiferromagnetic quantum spin chain whose edge spins are coupled to a set of three bosonic baths (one for each spin component) at different temperatures. The favorable numerical cost of solving integro-differential equations produced by SKFT+2PI framework with increasing number of spins, time steps or spatial dimensionality makes it a promising route for simulation of driven-dissipative systems in quantum computing or quantum magnonics and quantum spintronics in the presence of a single or multiple dissipative environments.

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