Long-range deformations in Gaussian States

• URL: http://arxiv.org/abs/2605.26932v1
• Date: Tue, 26 May 2026 12:25:22 GMT
• Title: Long-range deformations in Gaussian States
• Abstract summary: We modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings.<n>We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength.
• Score: 1.010795901725401
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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