Tame the Umklapp Processes in Real-Time Lattice Simulation for Hydrodynamics: An Ising Field Theory Study
Abstract
We calculate the real-time symmetric correlation function of the stress-energy tensor for a near-integrable Ising field theory consisting of three stable scalar particles via lattice Hamiltonian simulation. Using classical exact diagonalization and the matrix product state tensor network methods, we find that in the scaling region of the lattice theory, Umklapp processes that break continuum momentum conservation are suppressed and the sound modes of relativistic hydrodynamics emerge at long wavelength and late time in non-equilibrium dynamics. The extracted ratio of bulk viscosity to entropy density is ζ/s=3.06± 0.68 and the speed of sound is cs/c=0.76 ± 0.02 at the temperature T≈ 7.14 in units of the lowest stable particle's mass. Our study demonstrates the utility of real-time lattice Hamiltonian simulation for describing hydrodynamization and calculating transport coefficients nonperturbatively.
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BibTeX
@misc{yao2026tame,
title = {{Tame the Umklapp Processes in Real-Time Lattice Simulation for Hydrodynamics: An Ising Field Theory Study}},
author = {Xiaojun Yao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.09984},
eprint = {2606.09984},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.09984},
}
RIS
TY - UNPB
TI - Tame the Umklapp Processes in Real-Time Lattice Simulation for Hydrodynamics: An Ising Field Theory Study
AU - Xiaojun Yao
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2606.09984
UR - https://arxiv.org/abs/2606.09984
AB - We calculate the real-time symmetric correlation function of the stress-energy tensor for a near-integrable Ising field theory consisting of three stable scalar particles via lattice Hamiltonian simulation. Using classical exact diagonalization and the matrix product state tensor network methods, we find that in the scaling region of the lattice theory, Umklapp processes that break continuum momentum conservation are suppressed and the sound modes of relativistic hydrodynamics emerge at long wavelength and late time in non-equilibrium dynamics. The extracted ratio of bulk viscosity to entropy density is ζ/s=3.06± 0.68 and the speed of sound is c_s/c=0.76 ± 0.02 at the temperature T≈ 7.14 in units of the lowest stable particle's mass. Our study demonstrates the utility of real-time lattice Hamiltonian simulation for describing hydrodynamization and calculating transport coefficients nonperturbatively.
ER -