A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a 1/c expansion. The nth term of the expansion is of order 1/cn and takes into account all [n/2] + 1 parti...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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SciPost
2020
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| _version_ | 1826278184507670528 |
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| author | Essler, FHL Granet, E |
| author_facet | Essler, FHL Granet, E |
| author_sort | Essler, FHL |
| collection | OXFORD |
| description | We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a 1/c expansion. The nth term of the expansion is of order 1/cn and takes into account all [n/2] + 1 particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a "bare" 1/c expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order 1/c2. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these. |
| first_indexed | 2024-03-06T23:40:09Z |
| format | Journal article |
| id | oxford-uuid:6f07a0dc-0485-4fc8-b122-017be5fa414a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:40:09Z |
| publishDate | 2020 |
| publisher | SciPost |
| record_format | dspace |
| spelling | oxford-uuid:6f07a0dc-0485-4fc8-b122-017be5fa414a2022-03-26T19:28:10ZA systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6f07a0dc-0485-4fc8-b122-017be5fa414aEnglishSymplectic ElementsSciPost2020Essler, FHLGranet, EWe introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a 1/c expansion. The nth term of the expansion is of order 1/cn and takes into account all [n/2] + 1 particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a "bare" 1/c expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order 1/c2. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these. |
| spellingShingle | Essler, FHL Granet, E A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title | A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title_full | A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title_fullStr | A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title_full_unstemmed | A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title_short | A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model |
| title_sort | systematic 1 c expansion of form factor sums for dynamical correlations in the lieb liniger model |
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