Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910664656683008 |
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| author | Zakharov, V. A. Polla, S. Vela, A. Donís Emonts, P. Pacholski, M. J. Tworzydło, J. Beenakker, C. W. J. |
| author_facet | Zakharov, V. A. Polla, S. Vela, A. Donís Emonts, P. Pacholski, M. J. Tworzydło, J. Beenakker, C. W. J. |
| contents | To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdotσ$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the \textit{nonlocal} Hamiltonian of tangent fermions permits a \textit{local} generalized eigenproblem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions Zakharov, V. A. Polla, S. Vela, A. Donís Emonts, P. Pacholski, M. J. Tworzydło, J. Beenakker, C. W. J. Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdotσ$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the \textit{nonlocal} Hamiltonian of tangent fermions permits a \textit{local} generalized eigenproblem. |
| title | Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2407.06713 |