Real-time scattering in Ising field theory using matrix product states
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1.
Thomas Jefferson National Accelerator Facility
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2.
Amazon (United States)
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3.
University of Würzburg
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4.
California Institute of Technology
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5.
Perimeter Institute
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6.
ICTP South American Institute for Fundamental Research
Abstract
We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸₈ theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸₈ point in detail. Close to both the free fermion and 𝐸₈ theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
We thank Roland Farrell, Liam Fitzpatrick, Barak Gabai, Andrea Guerrieri, Alexandre Homrich, Joao Penedones, Federica Surace, Hao-Lan Xu, and Sasha Zamolodchikov for discussions and valuable comments on our draft, and Daniel Ranard for initial collaboration. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC operates Jefferson Lab. The research was also supported by 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. D.N. acknowledges support from the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration Grant No. 2021-2817, as well as the Würzburg-Dresden Cluster of Excellence “Complexity and Topology in Quantum Matter” (ct.qmat). J.P. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (Grants No. PHY-1733907 and No. PHY-2317110), the DOE QuantISED program through the theory consortium “Intersections of QIS and Theoretical Particle Physics” at Fermilab, the DOE Office of High Energy Physics (Grant No. DE-SC0018407), the DOE Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing (Grant No. DE-SC0020290), and the Air Force Office of Scientific Research (Grant No. FA9550-19-1-0360). Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. This work was additionally supported by a grant from the Simons Foundation (Simons Collaboration on the Nonperturbative Bootstrap Grant No. 488661) and ICTP-SAIFR FAPESP Grant No. 2016/01343-7 and FAPESP Grant No. 2017/03303-1.
Data Availability
The data that support the findings of this article are not publicly available upon publication because it is not technically feasible and/or the cost of preparing, depositing, and hosting the data would be prohibitive within the terms of this research project. The data are available from the authors upon reasonable request.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2411.13645 (arXiv)
Funding
- United States Department of Energy
- DE-AC05-06OR23177
- United States Department of Energy
- DE-SC0012704
- Heising-Simons Foundation
- 2021-2817
- National Science Foundation
- PHY-1733907
- National Science Foundation
- PHY-2317110
- United States Department of Energy
- DE-SC0018407
- United States Department of Energy
- DE-SC0020290
- United States Air Force Office of Scientific Research
- FA9550-19-1-0360
- Natural Sciences and Engineering Research Council
- Ministry of Research, Innovation and Science
- Simons Foundation
- 488661
- ICTP South American Institute for Fundamental Research
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- 2016/01343-7
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- 2017/03303-1
Dates
- Accepted
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2025-06-01