Sine-Gordon Model with Bosonic Tensor Networks: Continuum Matching and Soliton Scattering
Abstract
We use bosonic tensor networks to connect the lattice sine-Gordon model in the Hamiltonian formulation quantitatively to its continuum theory. Matching the lattice vertex operator to its conformal normalization at the free-boson ultraviolet fixed point yields the exact relation between the bare lattice coupling and the renormalized continuum mass parameter. The soliton mass then approaches Zamolodchikov's exact continuum prediction throughout the studied parameter range, without adjustable parameters. Using uniform matrix product states and a quasiparticle ansatz, we also recover the relativistic soliton dispersion and the two lightest breather masses at the percent level. We simulate real-time collisions of Gaussian soliton-antisoliton wave packets near a reflectionless point and extract the Wigner spatial displacement. We compare this displacement with the exact continuum prediction obtained from the momentum derivative of the transmission phase, recovering its characteristic rapidity dependence. Our bosonic simulations provide a foundation for nonintegrable extensions, offer lessons for renormalization in other Hamiltonian lattice field theories, including gauge theories, and provide benchmarks for continuous-variable quantum simulations.
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BibTeX
@misc{hechenberger2026sinegordon,
title = {{Sine-Gordon Model with Bosonic Tensor Networks: Continuum Matching and Soliton Scattering}},
author = {Florian Hechenberger and Tommaso Rainaldi and Felix Ringer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21846},
eprint = {2609.21846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sine-Gordon Model with Bosonic Tensor Networks: Continuum Matching and Soliton Scattering
AU - Florian Hechenberger
AU - Tommaso Rainaldi
AU - Felix Ringer
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21846
UR - https://arxiv.org/abs/2609.21846
AB - We use bosonic tensor networks to connect the lattice sine-Gordon model in the Hamiltonian formulation quantitatively to its continuum theory. Matching the lattice vertex operator to its conformal normalization at the free-boson ultraviolet fixed point yields the exact relation between the bare lattice coupling and the renormalized continuum mass parameter. The soliton mass then approaches Zamolodchikov's exact continuum prediction throughout the studied parameter range, without adjustable parameters. Using uniform matrix product states and a quasiparticle ansatz, we also recover the relativistic soliton dispersion and the two lightest breather masses at the percent level. We simulate real-time collisions of Gaussian soliton-antisoliton wave packets near a reflectionless point and extract the Wigner spatial displacement. We compare this displacement with the exact continuum prediction obtained from the momentum derivative of the transmission phase, recovering its characteristic rapidity dependence. Our bosonic simulations provide a foundation for nonintegrable extensions, offer lessons for renormalization in other Hamiltonian lattice field theories, including gauge theories, and provide benchmarks for continuous-variable quantum simulations.
ER -