Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
Abstract
We investigate the structure of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain using Lyapunov spectral analysis. We focus on the gapless phase of the Lyapunov spectrum, where the effective Hamiltonians behave differently from conventional critical Hamiltonians in isolated systems; the spectral gap closes faster than 1/L but slower than 1/L2 and the entanglement entropy grows as [ln(L)]2 where L is the system size. We find that the 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/L2. 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 rarely encountered in the ground states of conventional isolated quantum systems.
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BibTeX
@misc{mochizuki2026effective,
title = {{Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling}},
author = {Ken Mochizuki and Hisanori Oshima and Ryusuke Hamazaki and Yohei Fuji},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.04091},
eprint = {2609.04091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04091},
}
RIS
TY - UNPB
TI - Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
AU - Ken Mochizuki
AU - Hisanori Oshima
AU - Ryusuke Hamazaki
AU - Yohei Fuji
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.04091
UR - https://arxiv.org/abs/2609.04091
AB - We investigate the structure of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain using Lyapunov spectral analysis. We focus on the gapless phase of the Lyapunov spectrum, where the effective Hamiltonians behave differently from conventional critical Hamiltonians in isolated systems; the spectral gap closes faster than 1/L but slower than 1/L^2 and the entanglement entropy grows as [ln(L)]^2 where L is the system size. We find that the 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 rarely encountered in the ground states of conventional isolated quantum systems.
ER -