Su(2) Hubbard Model Achieves Asymptotic Quantum Many-Body Scar States in One Dimension
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The pursuit of understanding quantum many-body scars , rare, non-thermal eigenstates in interacting quantum systems , has taken a significant step forward with new research into the SU(2) Hubbard model. Daiki Hashimoto, Masaya Kunimi, and Tetsuro Nikuni, all from Tokyo University of Science, demonstrate the construction of these scars by embedding a specific subspace within a broader auxiliary Hilbert space and identifying a corresponding parent Hamiltonian. This work distinguishes itself from previous approaches by revealing that the parent Hamiltonian transforms into an SU(2) ferromagnetic Heisenberg model, allowing for gapless magnons that explicitly realise asymptotic many-body scar states. By mapping the problem onto a doublon-holon subspace and rigorously bounding entanglement entropy, the researchers not only expand the family of parent Hamiltonians capable of generating these scars, but also provide analytic, low-entanglement excitations within SU(2)-symmetric systems. This work distinguishes itself from previous approaches by revealing that the parent Hamiltonian transforms into an SU(2) ferromagnetic Heisenberg model, allowing for gapless magnons that explicitly realise asymptotic many-body scar states. By mapping the problem onto a doublon-holon subspace and rigorously bounding entanglement entropy, the researchers expand the family of parent Hamiltonians capable of generating these scars and provide analytic, low-entanglement excitations within SU(2)-symmetric systems. SU(N) Heisenberg Model and Algebraic Magnetisation Bound States The research extends the restricted spectrum-generating algebra to encompass multi-ladder systems, offering a more comprehensive approach to analysing complex quantum systems. Unlike prior applications of the parent-Hamiltonian scheme, this work demonstrates that the parent Hamiltonian corresponds to the SU(N) ferromagnetic Heisenberg model, rather than the spin-1/2 case, broadening the scope of applicable systems. Consequently, the gapless magnons within this model explicitly realise algebraic quantum magnetisation bound states (AQMBS) of the original system, providing insight into atypical quantum dynamics. By operating within the doublon, holon subspace, researchers derive this mapping and obtain the one-magnon dispersion for both periodic and open boundary conditions, detailing the excitation spectrum. Furthermore, the study proves three critical properties: orthogonality to the tower of scar states, vanishing energy variance in the thermodynamic limit, and subvolume entanglement entropy with rigorous matrix product state (MPS)/matrix product operator (MPO) bounds. These results broaden the applicability of the parent-Hamiltonian approach to a wider range of physical systems and provide a more complete understanding of their emergent behaviour. The findings offer new insights into the relationship between seemingly disparate models and the nature of quantum entanglement, potentially leading to advancements in quantum materials design. Many-Body Localization and Quantum Scar Coexistence Researchers have Scientists have achieved a significant breakthrough in understanding quantum many-body scars (QMBS) by constructing asymptotic QMBS (AQMBS) within one-dimensional SU(N) Hubbard chains. The research team embedded the scar subspace into an auxiliary Hilbert subspace and successfully identified a parent Hamiltonian, revealing that this Hamiltonian takes the form of the SU(N) ferromagnetic Heisenberg model, rather than the previously observed spin-1/2 case. This discovery demonstrates that the gapless magnons of this model explicitly realise AQMBS within the original system, opening new avenues for exploring atypical quantum dynamics. Experiments focused on the doublon-holon subspace, allowing the derivation of the one-magnon dispersion for both periodic and open boundary conditions.
Results demonstrate the orthogonality of the constructed states to the tower of scar states, a crucial property for establishing their distinct character. Measurements confirm a vanishing energy variance in the thermodynamic limit, indicating parametrically slow relaxation and diverging Mandelstam-Tamm bound, a hallmark of AQMBS behaviour. Rigorous bounds using matrix product states (MPS) and matrix product operators (MPO) were established, proving subvolume entanglement entropy scaling, which is essential for characterizing the low-entanglement nature of these excitations.
The team’s work broadens the family of parent Hamiltonians applicable to AQMBS beyond the conventional spin-1/2 models. The study meticulously mapped the system, obtaining the one-magnon dispersion relation for both periodic and open boundaries, providing detailed insight into the excitation spectrum. Data shows that the derived AQMBS states are not energy eigenstates of the original Hamiltonian, yet possess unique properties like low entanglement and characteristic energy variance. This breakthrough delivers analytic, low-entanglement excitations in SU(N)-symmetric systems, offering a powerful tool for investigating non-thermalizing behaviour in quantum materials. Scientists extended the restricted spectrum-generating algebra to accommodate multiple ladder operators, essential for analysing the SU(N) Hubbard model with its N-1 independent ladder operators. Tests prove the validity of this extension, providing a robust framework for understanding the algebraic underpinnings of AQMBS. SU(N) Hubbard Model Exhibits Low-Entanglement Scars This work extends the systematic construction of asymptotic many-body scars (AQMBS) to the SU(N) Hubbard model, for N greater than or equal to three. Researchers defined an enlarged overlap subspace and demonstrated that a tower of states forms exact quantum many-body scars within this framework, establishing a new family of parent Hamiltonians beyond the commonly studied spin-1/2 case. The key finding is that the parent Hamiltonian reduces to the ferromagnetic SU(N) Heisenberg model, hosting gapless magnon-like modes which represent explicit AQMBS of the original system. The study rigorously proves properties of these excitations, including orthogonality to the scar states, vanishing energy variance, and crucially, subvolume entanglement entropy, confirming their low-entanglement nature. Through matrix product state and matrix product operator constructions, the authors establish an upper bound on entanglement, demonstrating that these excitations genuinely constitute AQMBS above the SU(N) scar tower. The authors acknowledge limitations in experimental verification, noting the current difficulty in preparing the necessary η-pairing state required to observe these AQMBS. Future research directions include extending this construction to pyramid scar states found in multi-ladder systems, and pursuing experimental observation of AQMBS in SU(N) Hubbard models using existing techniques for preparing doublon states in optical lattices. While acknowledging the challenges, the authors suggest that advancements in preparing η-pairing states could ultimately enable the experimental confirmation of these theoretical findings. 👉 More information🗞 Construction of asymptotic quantum many-body scar states in the SU( ) Hubbard model🧠 ArXiv: https://arxiv.org/abs/2601.04640 Tags: