Finite-N Hamiltonian dynamics in long-range interacting systems

Quantum thermalization of closed systems -- i.e. the relaxation of local properties to their thermodynamic value along the Hamiltonian evolution -- is generically expected in non-integrable systems at finite energy density. In this work we show that quantum spin systems with at least one spin component coupled through long-range ferromagnetic interactions, and a second spin component coupled to a field, cannot in general thermalize to a paramagnetic state whenever they have a finite, negative energy per spin. The long-range interactions we consider decay as a power law of the distance, $\sim r^{-α}$ with $α< d$ , where $d$ is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.Quantum thermalization of closed systems -- i.e. the relaxation of local properties to their thermodynamic value along the Hamiltonian evolution -- is generically expected in non-integrable systems at finite energy density. In this work we show that quantum spin systems with at least one spin component coupled through long-range ferromagnetic interactions, and a second spin component coupled to a field, cannot in general thermalize to a paramagnetic state whenever they have a finite, negative energy per spin. The long-range interactions we consider decay as a power law of the distance, $\sim r^{-α}$ with $α< d$, where $d$ is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.

quant-pharXiv:2610.15530Oct 13, 20260 citations

Relaxation in Hamiltonian systems with long-range interactions

Yoshiyuki Y. Yamaguchi

cemeJan 1, 20020 citations

Dynamics of quantum systems with long-range interactions

Alexey Vyacheslavovich Gorshkov

Bulletin of the American Physical SocietyJun 1, 20200 citations

Exponentially slow heating in short and long-range interacting Floquet systems

Francisco Machado, Gregory D. Kahanamoku–Meyer, Dominic V. Else +2 more

The dynamics of Floquet Hamiltonians with short and long-range interactions are shown to exhibit a very long heating time scale that grows exponentially with the frequency of the drive. For times smaller than this heating time scale, the authors demonstrate that the dynamics of the system is well-approximated by evolution under a time-independent Hamiltonian, for both short-range interacting systems, in agreement with recent rigorous bounds, as well as for long-range interacting systems, where such results do not exist at present.The dynamics of Floquet Hamiltonians with short and long-range interactions are shown to exhibit a very long heating time scale that grows exponentially with the frequency of the drive. For times smaller than this heating time scale, the authors demonstrate that the dynamics of the system is well-approximated by evolution under a time-independent Hamiltonian, for both short-range interacting systems, in agreement with recent rigorous bounds, as well as for long-range interacting systems, where such results do not exist at present.

arXiv:1708.01620Physical Review ResearchDec 24, 201974 citations

Classical Hamiltonian Dynamics

Mark Linne

Elsevier eBooksJan 1, 20020 citations

\sim r^{-α}

with

α< d

, where

d

is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.