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Abstract Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space $$\mathcal {H}$$ H . Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in $$\mathcal {H}$$ H . This is achieved by discretising the sphere $$S_3$$ S 3 isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace–Beltrami operator on $$S_3$$ S 3 and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do.

Abstract We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10.1007/JHEP06(2021)043 , 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar $$\phi ^4$$ ϕ 4 theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes.