Helical Luttinger liquid on a space-time lattice
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908538995998720 |
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| author | Zakharov, V. A. Tworzydlo, J. Beenakker, C. W. J. Pacholski, M. J. |
| author_facet | Zakharov, V. A. Tworzydlo, J. Beenakker, C. W. J. Pacholski, M. J. |
| contents | The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results, because of the fermion-doubling obstruction: A local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here we show how to work around this obstruction, by discretizing both space and time to obtain a \textit{local} Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum Monte Carlo simulations that preserve the topological protection of an unpaired Dirac cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Helical Luttinger liquid on a space-time lattice Zakharov, V. A. Tworzydlo, J. Beenakker, C. W. J. Pacholski, M. J. Strongly Correlated Electrons Mesoscale and Nanoscale Physics The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results, because of the fermion-doubling obstruction: A local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here we show how to work around this obstruction, by discretizing both space and time to obtain a \textit{local} Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum Monte Carlo simulations that preserve the topological protection of an unpaired Dirac cone. |
| title | Helical Luttinger liquid on a space-time lattice |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.10828 |