On separation of variables for reflection algebras
Journal of Statistical Mechanics: Theory and Experiment, ISSN: 1742-5468, Vol: 2019, Issue: 9
2019
- 10Citations
- 3Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
We implement our new separation of variables (SoV) approach for open quantum integrable models associated to higher rank representations of the reflection algebras. We construct the (SoV) basis for the fundamental representations of the Y(gl) reflection algebra associated to general integrable boundary conditions. Moreover, we give the conditions on the boundary K-matrices allowing for the transfer matrix to be diagonalizable with simple spectrum. These SoV basis are then used to completely characterize the transfer matrix spectrum for the rank one and two reflection algebras. The rank one case is developed for both the rational and trigonometric fundamental representations of the 6-vertex reflection algebra. On the one hand, we extend the complete spectrum characterization to representations previously lying outside the SoV approach, e.g. those for which the standard algebraic Bethe Ansatz applies. On the other hand, we show that our new SoV construction can be reduced to the generalized Sklyanin's one whenever it is applicable. The rank two case is developed explicitly for the fundamental representations of the Y(gl) reflection algebra associated to general integrable boundary conditions. For both rank one and two our SoV approach leads to a complete characterization of the transfer matrix spectrum in terms of a set of polynomial solutions to the corresponding quantum spectral curve equation. Those are finite difference functional equations of order equal to the rank plus one, i.e. here two and three respectively for the Y(gl) and Y(gl) reflection algebras.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85083003745&origin=inward; http://dx.doi.org/10.1088/1742-5468/ab357a; https://iopscience.iop.org/article/10.1088/1742-5468/ab357a; https://iopscience.iop.org/article/10.1088/1742-5468/ab357a/pdf; https://dx.doi.org/10.1088/1742-5468/ab357a; https://validate.perfdrive.com/fb803c746e9148689b3984a31fccd902/captcha?ssa=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1742-5468%2Fab357a&ssb=df0f8bd2f5edf7cd1de2fe2e2ab998ebda5a65b0&ssc=MDI3MDQ5ZTAzYjcxLTcyNDgtZjNlNC03NDRiLWRhYzdkOTUy
IOP Publishing
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know