Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling

• URL: http://arxiv.org/abs/2609.04091v1
• Date: Thu, 03 Sep 2026 17:00:44 GMT
• Title: Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
• Abstract summary: We study the structures of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain.<n>We find that the corresponding effective Hamiltonians have random long-range power-law hoppings with nontrivial magnitude correlations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the structures of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain through the Lyapunov spectral analysis. We focus on a gapless phase characterized by finite-size scalings different from those in conventional critical and/or frustration-free systems; the spectral gap closing faster than $1/L$ but slower than $1/L^2$ and the entanglement entropy growing as $[\ln(L)]^2$ with $L$ being the system size. We find that the corresponding effective Hamiltonians have random long-range power-law hoppings with nontrivial magnitude correlations, rather than being independently and identically distributed. To elucidate the role of these non-Gaussian correlations, we construct random power-law hopping models that capture the essential features of the effective Hamiltonians. The spectral gaps of the constructed models decay faster than $1/L$ but slower than $1/L^2$. We find that, in the absence of hopping correlations, the ground-state entanglement exhibits $\ln(L)$ scaling. In the presence of correlations, by contrast, the entanglement entropy is enhanced and its system-size dependence is consistent with $[\ln(L)]^2$ scaling over the system sizes studied. These results suggest that correlations among long-range hopping magnitudes are responsible for the entanglement scaling that seldom appears in ground states of conventional isolated quantum systems.

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