Spin Hamiltonian for Quantum Simulation of Minimally Truncated 3+1D SU(2) Lattice Gauge Theory and Testing Eigenstate Thermalization
Abstract
We construct the spatial-gauge-singlet Hamiltonian of pure SU(2) lattice gauge theory in 3+1 dimensions (3+1D) on qubits under the minimal truncation jmax=1/2, building on previous work on the hyperhoneycomb lattice, and test the eigenstate thermalization hypothesis (ETH). By enforcing Gauss's law and exploiting the redundancy among gauge-invariant loop operators, we find the minimal set of independent loop variables that can be bijectively mapped onto qubits, and write the Hamiltonian as a sum of Pauli strings. An n× n× n lattice with fixed boundary conditions requires 2(n−1)3+3(n−1)2 qubits. We exactly diagonalize the Hamiltonian on a 2× 3× 3 lattice and identify the coupling range of quantum ergodicity from the level statistics. At the ergodic coupling g=0.3, we calculate the matrix elements of local energy density operators and the entanglement entropies of all eigenstates and find them consistent with the ETH. These results show that the 3+1D truncated SU(2) lattice gauge theory thermalizes in accordance with the ETH and provide a benchmark for future real-time quantum simulations of non-equilibrium dynamics.
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BibTeX
@misc{li2026spin,
title = {{Spin Hamiltonian for Quantum Simulation of Minimally Truncated $3+1$D SU(2) Lattice Gauge Theory and Testing Eigenstate Thermalization}},
author = {Ziyuan Li and Xiaojun Yao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36608},
eprint = {2610.36608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36608},
}
RIS
TY - UNPB
TI - Spin Hamiltonian for Quantum Simulation of Minimally Truncated 3+1D SU(2) Lattice Gauge Theory and Testing Eigenstate Thermalization
AU - Ziyuan Li
AU - Xiaojun Yao
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36608
UR - https://arxiv.org/abs/2610.36608
AB - We construct the spatial-gauge-singlet Hamiltonian of pure SU(2) lattice gauge theory in 3+1 dimensions (3+1D) on qubits under the minimal truncation j_max=1/2, building on previous work on the hyperhoneycomb lattice, and test the eigenstate thermalization hypothesis (ETH). By enforcing Gauss's law and exploiting the redundancy among gauge-invariant loop operators, we find the minimal set of independent loop variables that can be bijectively mapped onto qubits, and write the Hamiltonian as a sum of Pauli strings. An n× n× n lattice with fixed boundary conditions requires 2(n−1)^3+3(n−1)^2 qubits. We exactly diagonalize the Hamiltonian on a 2× 3× 3 lattice and identify the coupling range of quantum ergodicity from the level statistics. At the ergodic coupling g=0.3, we calculate the matrix elements of local energy density operators and the entanglement entropies of all eigenstates and find them consistent with the ETH. These results show that the 3+1D truncated SU(2) lattice gauge theory thermalizes in accordance with the ETH and provide a benchmark for future real-time quantum simulations of non-equilibrium dynamics.
ER -