Thermalization hierarchy from irreducible degrees of freedom

• URL: http://arxiv.org/abs/2607.03535v1
• Date: Fri, 03 Jul 2026 18:00:02 GMT
• Title: Thermalization hierarchy from irreducible degrees of freedom
• Abstract summary: We show that $D_$ controls thermalization continuously across the full spectrum of dynamical subspaces.<n>We also show that by selectively breaking symmetries, one can embed families of nonthermal eigenstates at prescribed entanglement levels into an otherwise ergodic spectrum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The decomposition of the Hilbert space of a quantum many-body system into the irreducible representations of its bond and commutant algebras yields a finer structure of dynamically isolated subspaces than the mere decomposition into symmetry sectors. While it has been recognized that subspaces associated with low bond-irrep dimensions $D_λ$ tend to violate the eigenstate thermalization hypothesis (ETH), here we show that $D_λ$ controls thermalization continuously across the full spectrum of dynamical subspaces. Using SU(2)-symmetric spin-1/2 chains as a paradigmatic example, we demonstrate that $\mathrm{log} \ D_λ$ quantitatively accounts for the average eigenstate entanglement entropy within each sector, establishing a thermalization hierarchy that interpolates from exact quantum many-body scars at $D_λ=1$ to volume-law ergodic states at large $D_λ$. To make this concrete, we introduce the notion of irreducible degrees of freedom (IDOF), defined as the number of independently-varying spatial coordinates parametrizing a many-body state within a given bond-algebra sector, which provides a microscopic interpretation of $D_λ$ and of the resulting thermalization hierarchy. Finally, we show that by selectively breaking symmetries while preserving chosen bond-algebra sectors, one can embed families of nonthermal eigenstates at prescribed entanglement levels into an otherwise ergodic spectrum, generalizing restricted spectrum-generating algebras from towers of individual states to entire dynamical subspaces.

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