Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914875198930944 |
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| author | Romiti, Simone Urbach, Carsten |
| author_facet | Romiti, Simone Urbach, Carsten |
| contents | We present a digitization scheme for the lattice $\mathrm{SU}(2)$ gauge theory Hamiltonian in the $\mathit{magnetic}$ $\mathit{basis}$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $\mathrm{SU}(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the kinetic part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11928 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations Romiti, Simone Urbach, Carsten High Energy Physics - Lattice Quantum Physics We present a digitization scheme for the lattice $\mathrm{SU}(2)$ gauge theory Hamiltonian in the $\mathit{magnetic}$ $\mathit{basis}$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $\mathrm{SU}(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the kinetic part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory. |
| title | Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations |
| topic | High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2311.11928 |