Galilean invariance restoration on the lattice

Abstract

We consider the breaking of Galilean invariance due to different lattice cutoff effects in moving frames and a nonlocal smearing parameter which is used in the construction of the nuclear lattice interaction. The dispersion relation and neutron-proton scattering phase shifts are used to investigate the Galilean invariance breaking effects and ways to restore it. For $S$-wave channels, ${}^1{S}_0$ and ${}^3{S}_1$, we present the neutron-proton scattering phase shifts in moving frames calculated using both Lüscher's formula and the spherical wall method, as well as the dispersion relation. For the $P$ and $D$ waves, we present the neutron-proton scattering phase shifts in moving frames calculated using the spherical wall method. We find that the Galilean invariance breaking effects stemming from the lattice artifacts partially cancel those caused by the nonlocal smearing parameter. Due to this cancellation, the Galilean invariance breaking effect is small, and the Galilean invariance can be restored by introducing Galilean invariance restoration operators.

arXiv comment13 pages, 7 figures

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Cited by in corpus (9)

• Essential elements for nuclear binding
• Lattice Effective Field Theory Simulations of Nuclei
• Ab Initio Simulations of Light Nuclear Systems Using Eigenvector Continuation and Auxiliary Field Monte Carlo
• Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice
• Effects of optical lattices on bright solitons in spin-orbit coupled Bose-Einstein condensates
• Charge-dependent nucleon-nucleon interaction at N${}^3$LO in nuclear lattice effective field theory
• Renormalization of a Contact Interaction on a Lattice
• Ab initio study of the halo structure in ${}^{11}$Be
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations