Floquet operator dynamics and orthogonal polynomials on the unit circle
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914259082936320 |
|---|---|
| author | Yeh, Hsiu-Chung Mitra, Aditi |
| author_facet | Yeh, Hsiu-Chung Mitra, Aditi |
| contents | Operator spreading under stroboscopic time evolution due to a unitary is studied. An operator Krylov space is constructed and related to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parameterizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC for persistent $m$-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the $Z_3$ clock model. The numerically obtained Krylov angles of the $Z_3$ clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Floquet operator dynamics and orthogonal polynomials on the unit circle Yeh, Hsiu-Chung Mitra, Aditi Strongly Correlated Electrons Quantum Physics Operator spreading under stroboscopic time evolution due to a unitary is studied. An operator Krylov space is constructed and related to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parameterizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC for persistent $m$-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the $Z_3$ clock model. The numerically obtained Krylov angles of the $Z_3$ clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior. |
| title | Floquet operator dynamics and orthogonal polynomials on the unit circle |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2506.20611 |