The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work, we derive the structure of ETH from a minimal dynamical principle, which we term the eigenstate typicality principle (ETP), together with general kinematic ingredients arising from entropy maximization, Hilbert-space geometry, and locality. ETP asserts that in quantum-chaotic systems, energy eigenstates are statistically indistinguishable, with respect to local measurements, from states drawn from the Haar measure on a narrow microcanonical shell. Within this framework, diagonal ETH arises from concentration of measure, provided that eigenstate typicality holds. The structure of off-diagonal matrix elements is then fixed by entropic scaling and the finite-time dynamical correlations of local observables, with ETP serving as the dynamical bridge to energy eigenstates, without invoking random-matrix assumptions. Our results establish ETH as a consequence of entropy, Hilbert-space geometry, and chaos-induced eigenstate typicality, and clarify its regime of validity across generic quantum-chaotic many-body systems, thereby deepening our understanding of quantum thermalization and the emergence of statistical mechanics from unitary many-body dynamics.The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work, we derive the structure of ETH from a minimal dynamical principle, which we term the eigenstate typicality principle (ETP), together with general kinematic ingredients arising from entropy maximization, Hilbert-space geometry, and locality. ETP asserts that in quantum-chaotic systems, energy eigenstates are statistically indistinguishable, with respect to local measurements, from states drawn from the Haar measure on a narrow microcanonical shell. Within this framework, diagonal ETH arises from concentration of measure, provided that eigenstate typicality holds. The structure of off-diagonal matrix elements is then fixed by entropic scaling and the finite-time dynamical correlations of local observables, with ETP serving as the dynamical bridge to energy eigenstates, without invoking random-matrix assumptions. Our results establish ETH as a consequence of entropy, Hilbert-space geometry, and chaos-induced eigenstate typicality, and clarify its regime of validity across generic quantum-chaotic many-body systems, thereby deepening our understanding of quantum thermalization and the emergence of statistical mechanics from unitary many-body dynamics.

cond-mat.stat-mechCross-listedarXiv:2512.13348Dec 16, 20250 citations

Thermalization in a closed many-body quantum system

Karamoko Soumahoro, Alison Valbuena, Roman Senkov

Bulletin of the American Physical SocietyMar 14, 20170 citations

Multipartite Entanglement Structure in the Eigenstate Thermalization Hypothesis

Marlon Brenes, Silvia Pappalardi, John Goold +1 more

We study the quantum Fisher information (QFI) and, thus, the multipartite entanglement structure of thermal pure states in the context of the eigenstate thermalization hypothesis (ETH). In both the canonical ensemble and the ETH, the quantum Fisher information may be explicitly calculated from the response functions. In the case of the ETH, we find that the expression of the QFI bounds the corresponding canonical expression from above. This implies that although average values and fluctuations of local observables are indistinguishable from their canonical counterpart, the entanglement structure of the state is starkly different; with the difference amplified, e.g., in the proximity of a thermal phase transition. We also provide a state-of-the-art numerical example of a situation where the quantum Fisher information in a quantum many-body system is extensive while the corresponding quantity in the canonical ensemble vanishes. Our findings have direct relevance for the entanglement structure in the asymptotic states of quenched many-body dynamics.We study the quantum Fisher information (QFI) and, thus, the multipartite entanglement structure of thermal pure states in the context of the eigenstate thermalization hypothesis (ETH). In both the canonical ensemble and the ETH, the quantum Fisher information may be explicitly calculated from the response functions. In the case of the ETH, we find that the expression of the QFI bounds the corresponding canonical expression from above. This implies that although average values and fluctuations of local observables are indistinguishable from their canonical counterpart, the entanglement structure of the state is starkly different; with the difference amplified, e.g., in the proximity of a thermal phase transition. We also provide a state-of-the-art numerical example of a situation where the quantum Fisher information in a quantum many-body system is extensive while the corresponding quantity in the canonical ensemble vanishes. Our findings have direct relevance for the entanglement structure in the asymptotic states of quenched many-body dynamics.

arXiv:1909.02980Physical Review LettersJan 31, 202050 citations

Many-body localization and quantum thermalization

Ehud Altman

Nature PhysicsSep 25, 201892 citations

Eigenstate thermalization at the edge of the many-body spectrum

Arnav Pushkar, Pranay Patil, Soumya Bera +2 more

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 $\mathbb{Z}_2$ -symmetric quantum spin- $\frac{1}{2}$ 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.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 $\mathbb{Z}_2$-symmetric quantum spin-$\frac{1}{2}$ 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.

cond-mat.str-elCross-listedarXiv:2609.38973Oct 1, 20260 citations

\mathbb{Z}_2

-symmetric quantum spin-

\frac{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.