Thermal Broadening of Phonon Spectral Function in Classical Lattice Models: Projective Truncation Approximation
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913700155228160 |
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| author | Jia, Hu-Wei Liu, Wen-Jun Wu, Yue-Hong Ma, Kou-Han Wang, Lei Tong, Ning-Hua |
| author_facet | Jia, Hu-Wei Liu, Wen-Jun Wu, Yue-Hong Ma, Kou-Han Wang, Lei Tong, Ning-Hua |
| contents | Thermal broadening of the quasi-particle peak in the spectral function is an important physical feature in many statistical systems, but it is difficult to calculate. To tackle this problem, we propose the $H$-expanded basis within the projective truncation approximation (PTA) of the Green's function equation of motion. A zeros-removing technique is introduced to stabilize the iterative solution of the PTA equations. Benchmarking calculations on the classical one-variable anharmonic oscillator model and the one-dimensional $ϕ^4$ lattice model show that the thermal broadened quasi-particle peak in the spectral function can be produced on a semi-quantitative level. Using this method, we discuss the low- and high- temperature power-law behaviors of the spectral width $Γ_k(T)$ of the one-dimensional $ϕ^4$ model, finding it in contradiction with the assumption of effective phonon theory. A short-chain limit of this model is also discovered. Issues of extending the $H$-expanded basis to quantum systems and of the applicability of the Debye formula for thermal conductivity are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermal Broadening of Phonon Spectral Function in Classical Lattice Models: Projective Truncation Approximation Jia, Hu-Wei Liu, Wen-Jun Wu, Yue-Hong Ma, Kou-Han Wang, Lei Tong, Ning-Hua Strongly Correlated Electrons Thermal broadening of the quasi-particle peak in the spectral function is an important physical feature in many statistical systems, but it is difficult to calculate. To tackle this problem, we propose the $H$-expanded basis within the projective truncation approximation (PTA) of the Green's function equation of motion. A zeros-removing technique is introduced to stabilize the iterative solution of the PTA equations. Benchmarking calculations on the classical one-variable anharmonic oscillator model and the one-dimensional $ϕ^4$ lattice model show that the thermal broadened quasi-particle peak in the spectral function can be produced on a semi-quantitative level. Using this method, we discuss the low- and high- temperature power-law behaviors of the spectral width $Γ_k(T)$ of the one-dimensional $ϕ^4$ model, finding it in contradiction with the assumption of effective phonon theory. A short-chain limit of this model is also discovered. Issues of extending the $H$-expanded basis to quantum systems and of the applicability of the Debye formula for thermal conductivity are discussed. |
| title | Thermal Broadening of Phonon Spectral Function in Classical Lattice Models: Projective Truncation Approximation |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.06384 |