We present a class of quantum dimer models on the kagome lattice with full translational invariance that feature a quantum many-body scar state of analytically known entanglement properties within their spectra. Using exact diagonalization on lattices of up to 60 sites, we show that nonscar states conform to the eigenstate thermalization hypothesis. Specifically, we show that energies are distributed according to the Gaussian ensemble expected of their respective symmetry sector, illustrate the existence of the scar from bipartite entanglement properties, and demonstrate revival phenomena in studies of fidelity dynamics.We present a class of quantum dimer models on the kagome lattice with full translational invariance that feature a quantum many-body scar state of analytically known entanglement properties within their spectra. Using exact diagonalization on lattices of up to 60 sites, we show that nonscar states conform to the eigenstate thermalization hypothesis. Specifically, we show that energies are distributed according to the Gaussian ensemble expected of their respective symmetry sector, illustrate the existence of the scar from bipartite entanglement properties, and demonstrate revival phenomena in studies of fidelity dynamics.

arXiv:2009.00022Physical review. B./Physical review. BSep 3, 202134 citations

Extent of the Z2 topological phase in the quantum dimer model

Marc Daniel Schulz, F. J. Burnell

Bulletin of the American Physical SocietyMar 14, 20160 citations

Symmetry-Protected Topological Structures in Quantum Many-Body Scar Subspaces

Chihiro Matsui, Thomas Quella, Naoto Tsuji

We investigate how symmetry-associated topological properties, originally defined for ground states, can be consistently extended to dynamically isolated subspaces of quantum many-body systems. Focusing on quantum many-body scars (QMBS), we show that a scar subspace is invariant under the relevant symmetries, and it can support well-defined topological properties inherited from an underlying symmetry-protected topological (SPT) ground state, even though individual scar states need not themselves be symmetric. We refer to such structures as SPT-like scar subspaces, emphasizing that the topological properties are defined at the level of the symmetry-invariant subspace rather than on a state-by-state basis. As a concrete example, we analyze the spin- $1$ Affleck--Kennedy--Lieb--Tasaki (AKLT) model, where a restricted spectrum-generating algebra (rSGA) generates a tower of QMBS on top of a nontrivial SPT ground state admitting a matrix product state (MPS) representation. We demonstrate that the resulting symmetry-invariant scar subspace inherits well-defined topological characteristics, encoded in bond-space symmetry representations, expectation values of symmetry-twist operators, and long-range string order in the dilute regime. We further show that these features persist in a broader class of models, including deformations and higher-spin generalizations that preserve the relevant symmetries and admit nontrivial SPT ground states with MPS representations. Our results provide a general framework in which symmetry-associated topological properties, while inherited from the ground state, are consistently realized at the level of symmetry-invariant nonthermal subspaces. This perspective clarifies how topological structures can be meaningfully defined beyond individual eigenstates.We investigate how symmetry-associated topological properties, originally defined for ground states, can be consistently extended to dynamically isolated subspaces of quantum many-body systems. Focusing on quantum many-body scars (QMBS), we show that a scar subspace is invariant under the relevant symmetries, and it can support well-defined topological properties inherited from an underlying symmetry-protected topological (SPT) ground state, even though individual scar states need not themselves be symmetric. We refer to such structures as SPT-like scar subspaces, emphasizing that the topological properties are defined at the level of the symmetry-invariant subspace rather than on a state-by-state basis. As a concrete example, we analyze the spin-$1$ Affleck--Kennedy--Lieb--Tasaki (AKLT) model, where a restricted spectrum-generating algebra (rSGA) generates a tower of QMBS on top of a nontrivial SPT ground state admitting a matrix product state (MPS) representation. We demonstrate that the resulting symmetry-invariant scar subspace inherits well-defined topological characteristics, encoded in bond-space symmetry representations, expectation values of symmetry-twist operators, and long-range string order in the dilute regime. We further show that these features persist in a broader class of models, including deformations and higher-spin generalizations that preserve the relevant symmetries and admit nontrivial SPT ground states with MPS representations. Our results provide a general framework in which symmetry-associated topological properties, while inherited from the ground state, are consistently realized at the level of symmetry-invariant nonthermal subspaces. This perspective clarifies how topological structures can be meaningfully defined beyond individual eigenstates.

cond-mat.str-elCross-listedarXiv:2512.11216Dec 15, 20250 citations

Topological Methods for Description of Quantum Many-Body Systems

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek +1 more

Oxford University Press eBooksSep 25, 20030 citations

Strongly-tilted field induced Hamiltonian dimerization and nested quantum scars in the 1D spinless Fermi-Hubbard model

Wei-Jie Huang, Yu‐Biao Wu, Guang‐Can Guo +2 more

Abstract We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective Hamiltonian, and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization, which are composed of two distinct sets of constrained nearest-neighbor hopping terms: one set acting exclusively on odd bonds and the other on even bonds. Specifically it is shown that each part can be independently mapped onto the well-known PXP model, therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model. As a consequence, we numerically demonstrate this system can host the so-called quantum many-body scars, which present dynamical revivals and ergodicity-breaking behaviors. However in sharp contrast with traditional quantum many-body scars, here the scarring states in our model driven by different parts of Hamiltonian will revive in different periods, and those of double parts can display a biperiodic revival pattern, both originating from the Hamiltonian dimerization. Besides, the condition of off-resonance is also discussed and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics. Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.Abstract We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective Hamiltonian, and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization, which are composed of two distinct sets of constrained nearest-neighbor hopping terms: one set acting exclusively on odd bonds and the other on even bonds. Specifically it is shown that each part can be independently mapped onto the well-known PXP model, therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model. As a consequence, we numerically demonstrate this system can host the so-called quantum many-body scars, which present dynamical revivals and ergodicity-breaking behaviors. However in sharp contrast with traditional quantum many-body scars, here the scarring states in our model driven by different parts of Hamiltonian will revive in different periods, and those of double parts can display a biperiodic revival pattern, both originating from the Hamiltonian dimerization. Besides, the condition of off-resonance is also discussed and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics. Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.

arXiv:2402.18828Chinese Physics LettersJul 1, 20251 citation

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Affleck--Kennedy--Lieb--Tasaki (AKLT) model, where a restricted spectrum-generating algebra (rSGA) generates a tower of QMBS on top of a nontrivial SPT ground state admitting a matrix product state (MPS) representation. We demonstrate that the resulting symmetry-invariant scar subspace inherits well-defined topological characteristics, encoded in bond-space symmetry representations, expectation values of symmetry-twist operators, and long-range string order in the dilute regime. We further show that these features persist in a broader class of models, including deformations and higher-spin generalizations that preserve the relevant symmetries and admit nontrivial SPT ground states with MPS representations. Our results provide a general framework in which symmetry-associated topological properties, while inherited from the ground state, are consistently realized at the level of symmetry-invariant nonthermal subspaces. This perspective clarifies how topological structures can be meaningfully defined beyond individual eigenstates.