Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polyn...
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| Format: | Article |
| Language: | English |
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SciPost
2017-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.3.1.003 |
| _version_ | 1828884247568449536 |
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| author | Guillaume Lang, Frank Hekking, Anna Minguzzi |
| author_facet | Guillaume Lang, Frank Hekking, Anna Minguzzi |
| author_sort | Guillaume Lang, Frank Hekking, Anna Minguzzi |
| collection | DOAJ |
| description | We study the ground-state properties and excitation spectrum of the
Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact
interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by
using an analytic method based on a series expansion on orthogonal polynomials
developed in \cite{Ristivojevic} and push the expansion to an unprecedented
order. By a careful analysis of the mathematical structure of the series
expansion, we make a conjecture for the analytic exact result at zero
temperature and show that the partially resummed expressions thereby obtained
compete with accurate numerical calculations. This allows us to evaluate the
density of quasi-momenta, the ground-state energy, the local two-body
correlation function and Tan's contact. Then, we study the two branches of the
excitation spectrum. Using a general analysis of their properties and
symmetries, we obtain novel analytical expressions at arbitrary interaction
strength which are found to be extremely accurate in a wide range of
intermediate to strong interactions. |
| first_indexed | 2024-12-13T11:03:49Z |
| format | Article |
| id | doaj.art-bd787bacef514fc2bbeb58875c66ea1e |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-13T11:03:49Z |
| publishDate | 2017-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-bd787bacef514fc2bbeb58875c66ea1e2022-12-21T23:49:09ZengSciPostSciPost Physics2542-46532017-07-013100310.21468/SciPostPhys.3.1.003Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solutionGuillaume Lang, Frank Hekking, Anna MinguzziWe study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.https://scipost.org/SciPostPhys.3.1.003 |
| spellingShingle | Guillaume Lang, Frank Hekking, Anna Minguzzi Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution SciPost Physics |
| title | Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution |
| title_full | Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution |
| title_fullStr | Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution |
| title_full_unstemmed | Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution |
| title_short | Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution |
| title_sort | ground state energy and excitation spectrum of the lieb liniger model accurate analytical results and conjectures about the exact solution |
| url | https://scipost.org/SciPostPhys.3.1.003 |
| work_keys_str_mv | AT guillaumelangfrankhekkingannaminguzzi groundstateenergyandexcitationspectrumofthelieblinigermodelaccurateanalyticalresultsandconjecturesabouttheexactsolution |