Abstract
We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.
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Acknowledgments
We are grateful to Hank Lamm, Phiala Shanahan, Paulo Bedaque, Jacob Bringewatt, Connor Mooney and Lucas Brady for their time and discussions. NCW is supported in part by: the U.S. Department of Energy, Office of Science under grant Contract Numbers DE-SC0011090 and DE-SC0021006, the Simons Foundation grant 994314 (Simons Collaboration on Confinement and QCD Strings), and the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-Design Center for Quantum Advantage under Contract No. DE-SC0012704
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ArXiv ePrint: 2310.19761
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Warrington, N.C. Real-time spin systems from lattice field theory. J. High Energ. Phys. 2023, 156 (2023). https://doi.org/10.1007/JHEP12(2023)156
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DOI: https://doi.org/10.1007/JHEP12(2023)156