Eigenstate thermalization at the edge of the many-body spectrum
Abstract
It is well-known that thermalization breaks down in presence of an extensive number of symmetries or conservation laws that are mutually compatible or commuting with each other. We ask here how an extensive number of mutually incompatible local symmetries govern eigenstate thermalization (ETH). We will investigate this through models within the class of bond-dependent ℤ2-symmetric quantum spin-1/2 Hamiltonians that naturally admit this structure. This leads to exponentially large degeneracies in the spectrum governed by the incompatible symmetry structure. Here, using spectral diagnostics, we show that non-integrability can survive despite extensively many conserved quantities when they are incompatible. Furthermore, we show that ETH behavior persists deep into the many-body spectral edge due to this structure. In other words, incompatible local symmetries enable a mechanism to obtain enough thermodynamic entropy at low excitation energy densities to make ETH operational or predictive near the ground state.
Related
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BibTeX
@misc{pushkar2026eigenstate,
title = {{Eigenstate thermalization at the edge of the many-body spectrum}},
author = {Arnav Pushkar and Pranay Patil and Soumya Bera and Masaki Tezuka and Sumiran Pujari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38973},
eprint = {2609.38973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38973},
}
RIS
TY - UNPB
TI - Eigenstate thermalization at the edge of the many-body spectrum
AU - Arnav Pushkar
AU - Pranay Patil
AU - Soumya Bera
AU - Masaki Tezuka
AU - Sumiran Pujari
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38973
UR - https://arxiv.org/abs/2609.38973
AB - It is well-known that thermalization breaks down in presence of an extensive number of symmetries or conservation laws that are mutually compatible or commuting with each other. We ask here how an extensive number of mutually incompatible local symmetries govern eigenstate thermalization (ETH). We will investigate this through models within the class of bond-dependent ℤ_2-symmetric quantum spin-1/2 Hamiltonians that naturally admit this structure. This leads to exponentially large degeneracies in the spectrum governed by the incompatible symmetry structure. Here, using spectral diagnostics, we show that non-integrability can survive despite extensively many conserved quantities when they are incompatible. Furthermore, we show that ETH behavior persists deep into the many-body spectral edge due to this structure. In other words, incompatible local symmetries enable a mechanism to obtain enough thermodynamic entropy at low excitation energy densities to make ETH operational or predictive near the ground state.
ER -