Long-range deformations in Gaussian States
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916049759240192 |
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| author | Pereira, Francisco Manoj, Nandagopal Murciano, Sara |
| author_facet | Pereira, Francisco Manoj, Nandagopal Murciano, Sara |
| contents | Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings that enhance pairing correlations, typically of the form $1/r^α$, where $r$ is the distance between two sites. As the state remains Gaussian, entanglement and correlation functions can be computed analytically. We find that the decay exponent $α$ controls three distinct infrared regimes: for $α>1$, the deformation produces only smooth crossovers at finite deformation strength, while the topological regime is reached only asymptotically as the deformation strength tends to infinity. At $α=1$, the deformation induces an immediate flow to the topological phase: an infinitesimal deformation strength drives the system to a topological regime, and in a particular case, an emergent Kramers-Wannier symmetry enforces Ising-like scaling at long distances. For $α<1$, the deformed state shows the same critical-like behavior for all non-zero deformation strength. We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-range deformations in Gaussian States Pereira, Francisco Manoj, Nandagopal Murciano, Sara Statistical Mechanics High Energy Physics - Theory Quantum Physics Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings that enhance pairing correlations, typically of the form $1/r^α$, where $r$ is the distance between two sites. As the state remains Gaussian, entanglement and correlation functions can be computed analytically. We find that the decay exponent $α$ controls three distinct infrared regimes: for $α>1$, the deformation produces only smooth crossovers at finite deformation strength, while the topological regime is reached only asymptotically as the deformation strength tends to infinity. At $α=1$, the deformation induces an immediate flow to the topological phase: an infinitesimal deformation strength drives the system to a topological regime, and in a particular case, an emergent Kramers-Wannier symmetry enforces Ising-like scaling at long distances. For $α<1$, the deformed state shows the same critical-like behavior for all non-zero deformation strength. We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength. |
| title | Long-range deformations in Gaussian States |
| topic | Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2605.26932 |