Fast Real-Axis Eliashberg Calculations: Full-bandwidth solutions beyond the constant density of states approximation
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| Main Authors: | , , , , , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910058975068160 |
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| author | Simon, Alejandro Shi, James Spath, Dominik Kogler, Eva Foster, Reed Batson, Emma Ferreira, Pedro N. Sahoo, Mihir Keathley, Phillip D. Pickett, Warren E. Prasankumar, Rohit Berggren, Karl K. Heil, Christoph |
| author_facet | Simon, Alejandro Shi, James Spath, Dominik Kogler, Eva Foster, Reed Batson, Emma Ferreira, Pedro N. Sahoo, Mihir Keathley, Phillip D. Pickett, Warren E. Prasankumar, Rohit Berggren, Karl K. Heil, Christoph |
| contents | Experimentally relevant signatures of superconductivity require access to real-frequency quantities, such as the spectral functions, optical response, and transport properties, yet Migdal-Eliashberg calculations are commonly performed on the imaginary axis and then analytically continued, a step that is numerically delicate and can obscure physically relevant spectral features. Here we present a practical route to solving the finite-temperature Migdal-Eliashberg equations directly on the real-frequency axis, while retaining the effects from the full-bandwidth electronic structure. Our formulation accounts for particle-hole asymmetry through an energy-dependent electronic density of states, avoiding the constant density of states approximation often used in real-axis calculations, and includes a static screened Coulomb contribution. We introduce an efficient numerical technique to solve the Migdal-Eliashberg integrals whose computational cost scales linearly with the real-frequency grid, making high-resolution, full-bandwidth real-axis calculations feasible and providing direct access to the interacting Green's function and derived observables without analytic continuation. As an illustration, we apply the method to H$_{3}$S, where a van-Hove singularity near the Fermi level produces strong particle-hole asymmetry. The full-bandwidth solution yields noticeably different spectra than the constant density of states approximation and brings the superconducting gap and lineshapes into closer agreement with experiment, highlighting when band-structure details are essential. Furthermore, the methods presented here open the door to time-dependent, nonequilibrium simulations within Eliashberg theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_18199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Real-Axis Eliashberg Calculations: Full-bandwidth solutions beyond the constant density of states approximation Simon, Alejandro Shi, James Spath, Dominik Kogler, Eva Foster, Reed Batson, Emma Ferreira, Pedro N. Sahoo, Mihir Keathley, Phillip D. Pickett, Warren E. Prasankumar, Rohit Berggren, Karl K. Heil, Christoph Superconductivity Experimentally relevant signatures of superconductivity require access to real-frequency quantities, such as the spectral functions, optical response, and transport properties, yet Migdal-Eliashberg calculations are commonly performed on the imaginary axis and then analytically continued, a step that is numerically delicate and can obscure physically relevant spectral features. Here we present a practical route to solving the finite-temperature Migdal-Eliashberg equations directly on the real-frequency axis, while retaining the effects from the full-bandwidth electronic structure. Our formulation accounts for particle-hole asymmetry through an energy-dependent electronic density of states, avoiding the constant density of states approximation often used in real-axis calculations, and includes a static screened Coulomb contribution. We introduce an efficient numerical technique to solve the Migdal-Eliashberg integrals whose computational cost scales linearly with the real-frequency grid, making high-resolution, full-bandwidth real-axis calculations feasible and providing direct access to the interacting Green's function and derived observables without analytic continuation. As an illustration, we apply the method to H$_{3}$S, where a van-Hove singularity near the Fermi level produces strong particle-hole asymmetry. The full-bandwidth solution yields noticeably different spectra than the constant density of states approximation and brings the superconducting gap and lineshapes into closer agreement with experiment, highlighting when band-structure details are essential. Furthermore, the methods presented here open the door to time-dependent, nonequilibrium simulations within Eliashberg theory. |
| title | Fast Real-Axis Eliashberg Calculations: Full-bandwidth solutions beyond the constant density of states approximation |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2603.18199 |