Exact large-scale correlations in integrable systems out of equilibrium
Using the theory of generalized hydrodynamics (GHD), we derive exact Euler-scale dynamical two-point correlation functions of conserved densities and currents in inhomogeneous, non-stationary states of many-body integrable systems with weak space-time variations. This extends previous works to i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2018-11-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.5.5.054 |
| _version_ | 1811315534046691328 |
|---|---|
| author | Benjamin Doyon |
| author_facet | Benjamin Doyon |
| author_sort | Benjamin Doyon |
| collection | DOAJ |
| description | Using the theory of generalized hydrodynamics (GHD), we derive exact
Euler-scale dynamical two-point correlation functions of conserved densities
and currents in inhomogeneous, non-stationary states of many-body integrable
systems with weak space-time variations. This extends previous works to
inhomogeneous and non-stationary situations. Using GHD projection operators, we
further derive formulae for Euler-scale two-point functions of arbitrary local
fields, purely from the data of their homogeneous one-point functions. These
are new also in homogeneous generalized Gibbs ensembles. The technique is based
on combining a fluctuation-dissipation principle along with the exact solution
by characteristics of GHD, and gives a recursive procedure able to generate
$n$-point correlation functions. Owing to the universality of GHD, the results
are expected to apply to quantum and classical integrable field theory such as
the sinh-Gordon model and the Lieb-Liniger model, spin chains such as the XXZ
and Hubbard models, and solvable classical gases such as the hard rod gas and
soliton gases. In particular, we find Leclair-Mussardo-type infinite
form-factor series in integrable quantum field theory, and exact Euler-scale
two-point functions of exponential fields in the sinh-Gordon model and of
powers of the density field in the Lieb-Liniger model. We also analyze
correlations in the partitioning protocol, extract large-time asymptotics, and,
in free models, derive all Euler-scale $n$-point functions. |
| first_indexed | 2024-04-13T11:31:41Z |
| format | Article |
| id | doaj.art-5c99bcd4e105467380f538bd77b42f76 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-13T11:31:41Z |
| publishDate | 2018-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-5c99bcd4e105467380f538bd77b42f762022-12-22T02:48:33ZengSciPostSciPost Physics2542-46532018-11-015505410.21468/SciPostPhys.5.5.054Exact large-scale correlations in integrable systems out of equilibriumBenjamin DoyonUsing the theory of generalized hydrodynamics (GHD), we derive exact Euler-scale dynamical two-point correlation functions of conserved densities and currents in inhomogeneous, non-stationary states of many-body integrable systems with weak space-time variations. This extends previous works to inhomogeneous and non-stationary situations. Using GHD projection operators, we further derive formulae for Euler-scale two-point functions of arbitrary local fields, purely from the data of their homogeneous one-point functions. These are new also in homogeneous generalized Gibbs ensembles. The technique is based on combining a fluctuation-dissipation principle along with the exact solution by characteristics of GHD, and gives a recursive procedure able to generate $n$-point correlation functions. Owing to the universality of GHD, the results are expected to apply to quantum and classical integrable field theory such as the sinh-Gordon model and the Lieb-Liniger model, spin chains such as the XXZ and Hubbard models, and solvable classical gases such as the hard rod gas and soliton gases. In particular, we find Leclair-Mussardo-type infinite form-factor series in integrable quantum field theory, and exact Euler-scale two-point functions of exponential fields in the sinh-Gordon model and of powers of the density field in the Lieb-Liniger model. We also analyze correlations in the partitioning protocol, extract large-time asymptotics, and, in free models, derive all Euler-scale $n$-point functions.https://scipost.org/SciPostPhys.5.5.054 |
| spellingShingle | Benjamin Doyon Exact large-scale correlations in integrable systems out of equilibrium SciPost Physics |
| title | Exact large-scale correlations in integrable systems out of equilibrium |
| title_full | Exact large-scale correlations in integrable systems out of equilibrium |
| title_fullStr | Exact large-scale correlations in integrable systems out of equilibrium |
| title_full_unstemmed | Exact large-scale correlations in integrable systems out of equilibrium |
| title_short | Exact large-scale correlations in integrable systems out of equilibrium |
| title_sort | exact large scale correlations in integrable systems out of equilibrium |
| url | https://scipost.org/SciPostPhys.5.5.054 |
| work_keys_str_mv | AT benjamindoyon exactlargescalecorrelationsinintegrablesystemsoutofequilibrium |