Role of Noise on Defect Formation and Correlations in a Long-Range Ising Model Under Adiabatic Driving
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910928262397952 |
|---|---|
| author | Dhara, Santanu Gangadharaiah, Suhas |
| author_facet | Dhara, Santanu Gangadharaiah, Suhas |
| contents | We study an exactly solvable long-range (LR) transverse-field Ising model (TFIM) with a power-law decaying interaction characterized by a decay exponent α. In the thermodynamic limit, the system is adiabatically driven in the presence of noise, from a paramagnetic phase with all spins down to one with all spins up. Our study examines the role of long-range interactions on the defect density, its distribution, and spin correlations, comparing noisy and noiseless scenarios. In the noiseless case, within the long-range regime, the steady-state properties are primarily influenced by modes near the k = π region. However, in the presence of noise, the dominant contributions shift to the modes near k = 0. This differs from the SR model, where previous studies have shown that modes around k = π/2 play a significant role under noisy conditions. In the absence of noise, defect density scales as $n\propto τ_Q^{-1/2}$, implying scaling exponent independent of decay exponent. However, we find that decreasing the value of α (i.e., increasing the range) enhances the defect density, whereas in the presence of noise, it is suppressed. In the LR regime, two-point fermionic correlators initially exhibit Gaussian decay, followed by quadratic suppression instead of power-law decay for both noisy and noiseless scenarios. Meanwhile, spin correlators, expressed as a string of fermionic operators, undergo purely exponential decay with no crossover behavior. Furthermore, our analysis of defect formation reveals the influence of LR interaction on the kink-number distribution and its cumulants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Role of Noise on Defect Formation and Correlations in a Long-Range Ising Model Under Adiabatic Driving Dhara, Santanu Gangadharaiah, Suhas Other Condensed Matter We study an exactly solvable long-range (LR) transverse-field Ising model (TFIM) with a power-law decaying interaction characterized by a decay exponent α. In the thermodynamic limit, the system is adiabatically driven in the presence of noise, from a paramagnetic phase with all spins down to one with all spins up. Our study examines the role of long-range interactions on the defect density, its distribution, and spin correlations, comparing noisy and noiseless scenarios. In the noiseless case, within the long-range regime, the steady-state properties are primarily influenced by modes near the k = π region. However, in the presence of noise, the dominant contributions shift to the modes near k = 0. This differs from the SR model, where previous studies have shown that modes around k = π/2 play a significant role under noisy conditions. In the absence of noise, defect density scales as $n\propto τ_Q^{-1/2}$, implying scaling exponent independent of decay exponent. However, we find that decreasing the value of α (i.e., increasing the range) enhances the defect density, whereas in the presence of noise, it is suppressed. In the LR regime, two-point fermionic correlators initially exhibit Gaussian decay, followed by quadratic suppression instead of power-law decay for both noisy and noiseless scenarios. Meanwhile, spin correlators, expressed as a string of fermionic operators, undergo purely exponential decay with no crossover behavior. Furthermore, our analysis of defect formation reveals the influence of LR interaction on the kink-number distribution and its cumulants. |
| title | Role of Noise on Defect Formation and Correlations in a Long-Range Ising Model Under Adiabatic Driving |
| topic | Other Condensed Matter |
| url | https://arxiv.org/abs/2505.02661 |