Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. Identifying systems where at least some eigenstates are nonthermal is an outstanding question. In this Letter we show that interacting quantum models that have a nullspace—a degenerate subspace of eigenstates at zero energy (zero modes), which corresponds to infinite temperature, provide a route to nonthermal eigenstates. We analytically show the existence of a zero mode which can be represented as a matrix product state for a certain class of local Hamiltonians. In the more general case we use a subspace disentangling algorithm to generate an orthogonal basis of zero modes characterized by increasing entanglement entropy. We show evidence for an area-law entanglement scaling of the least-entangled zero mode in the broad parameter regime, leading to a conjecture that all local Hamiltonians with the nullspace feature zero modes with area-law entanglement scaling and, as such, break the strong thermalization hypothesis. Finally, we find zero modes in constrained models and propose a setup for observing their experimental signatures.
Physical Review Letters
We acknowledge useful discussions with V. Gritsev and A. Garkun and suggestions on implementation of the PPXPP model by D. Bluvstein. A. M. and M. S. were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899)
Karle V, Serbyn M, Michailidis A. Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. 2021;127(6). doi:10.1103/physrevlett.127.060602
Karle, V., Serbyn, M., & Michailidis, A. (2021). Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. American Physical Society. https://doi.org/10.1103/physrevlett.127.060602
Karle, Volker, Maksym Serbyn, and Alexios Michailidis. “Area-Law Entangled Eigenstates from Nullspaces of Local Hamiltonians.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/physrevlett.127.060602.
V. Karle, M. Serbyn, and A. Michailidis, “Area-law entangled eigenstates from nullspaces of local Hamiltonians,” Physical Review Letters, vol. 127, no. 6. American Physical Society, 2021.
Karle V, Serbyn M, Michailidis A. 2021. Area-law entangled eigenstates from nullspaces of local Hamiltonians. Physical Review Letters. 127(6), 060602.
Karle, Volker, et al. “Area-Law Entangled Eigenstates from Nullspaces of Local Hamiltonians.” Physical Review Letters, vol. 127, no. 6, 060602, American Physical Society, 2021, doi:10.1103/physrevlett.127.060602.
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