KPZ scaling from the Krylov space
Abstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation function...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-09-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2024)021 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850169607128612864 |
|---|---|
| author | Alexander Gorsky Sergei Nechaev Alexander Valov |
| author_facet | Alexander Gorsky Sergei Nechaev Alexander Valov |
| author_sort | Alexander Gorsky |
| collection | DOAJ |
| description | Abstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time t E ∗ $$ {t}_E^{\ast } $$ = c cr K, for the Krylov chain of finite length K, and c cr = O(1). In particular, we find a scaling ~ K 1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K −2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/N) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography. |
| format | Article |
| id | doaj-art-5f0c595b4fbf4ac28cf16e29009bca4f |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-5f0c595b4fbf4ac28cf16e29009bca4f2025-08-20T02:20:41ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024913310.1007/JHEP09(2024)021KPZ scaling from the Krylov spaceAlexander Gorsky0Sergei Nechaev1Alexander Valov2Institute for Information Transmission Problems RASLPTMS, CNRS — Université Paris SaclayRacah Institute of Physics, Hebrew University of JerusalemAbstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time t E ∗ $$ {t}_E^{\ast } $$ = c cr K, for the Krylov chain of finite length K, and c cr = O(1). In particular, we find a scaling ~ K 1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K −2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/N) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.https://doi.org/10.1007/JHEP09(2024)0212D GravityMatrix ModelsNonperturbative EffectsStochastic Processes |
| spellingShingle | Alexander Gorsky Sergei Nechaev Alexander Valov KPZ scaling from the Krylov space Journal of High Energy Physics 2D Gravity Matrix Models Nonperturbative Effects Stochastic Processes |
| title | KPZ scaling from the Krylov space |
| title_full | KPZ scaling from the Krylov space |
| title_fullStr | KPZ scaling from the Krylov space |
| title_full_unstemmed | KPZ scaling from the Krylov space |
| title_short | KPZ scaling from the Krylov space |
| title_sort | kpz scaling from the krylov space |
| topic | 2D Gravity Matrix Models Nonperturbative Effects Stochastic Processes |
| url | https://doi.org/10.1007/JHEP09(2024)021 |
| work_keys_str_mv | AT alexandergorsky kpzscalingfromthekrylovspace AT sergeinechaev kpzscalingfromthekrylovspace AT alexandervalov kpzscalingfromthekrylovspace |