Topological quantum pump of strongly interacting fermions in coupled chains

Voorden, Bart van; Schoutens, Kareljan

doi:10.1088/1367-2630/aaf748

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…[5], Fendley suggests applying this solution method to the cooper pair model of Refs. [72,73], which represents one other such fermion model. However, the frustration graph of this model has even holes, and so is ineligible for solution by our method.…”

Section: Discussionmentioning

confidence: 99%

Free Fermions Behind the Disguise

Elman

Chapman

Flammia

2021

Commun. Math. Phys.

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An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph G of a Hamiltonian H, i.e., the network of anticommutation relations between the Pauli terms in H in a given basis. Specifically, when G is (even-hole, claw)-free, we construct an explicit free-fermion solution for H using only this structure of G, even when no Jordan-Wigner transformation exists. The solution method is generic in that it applies for any values of the couplings. This mapping generalizes both the classic Lieb-Schultz-Mattis solution of the XY model and an exact solution of a spin chain recently given by Fendley, dubbed "free fermions in disguise." Like Fendley's original example, the free-fermion operators that solve the model are generally highly nonlinear and nonlocal, but can nonetheless be found explicitly using a transfer operator defined in terms of the independent sets of G. The associated single-particle energies are calculated using the roots of the independence polynomial of G, which are guaranteed to be real by a result of Chudnovsky and Seymour. Furthermore, recognizing (even-hole, claw)-free graphs can be done in polynomial time, so recognizing when a spin model is solvable in this way is efficient. In a crucial step to proving our result, we additionally prove that there exists a hierarchy of commuting conserved charges for models whose frustration graphs are claw-free only, and hence these models are integrable. Finally, we give several example families of solvable and integrable models for which no Jordan-Wigner solution exists, and we give a detailed analysis of such a spin chain having 4-body couplings using this method.

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Section: Discussionmentioning

confidence: 99%

Free Fermions Behind the Disguise

Elman

Chapman

Flammia

2021

Commun. Math. Phys.

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“…Interactions between particles cause novel correlation and entanglement, which may introduce rich correlated topological phenomena [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Understanding the interaction effect in topological pumping could open a window to the largely unexplored field.…”

Section: Introductionmentioning

confidence: 99%

Topological pumping induced by spatiotemporal modulation of interaction

Huang,

Ke,

Liu

et al. 2024

Phys. Scr.

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Particle-particle interaction provides a new degree of freedom to induce novel topological phenomena. Here, we propose to use spatiotemporal modulation of interaction to realize topological pumping without a single-particle counterpart. Because the modulation breaks time-reversal symmetry, the multiparticle energy bands of bound states have none-zero Chern number, and support topological bound edge states. In a Thouless pump, a bound state that uniformly occupies a topological energy band can be shifted by integer unit cells per cycle, consistent with the corresponding Chern number. We can also realize topological pumping of bound edge state fromone end to another. The entanglement entropy between particles rapidly increases at transition points, which is related to the spatial spread of a bounded pair. In addition, we propose to realize hybridized pumping with fractional displacement per cycle by adding an extra tilt potential to separate topological pumping of the bound state and Bloch oscillations of single particle. Our work could trigger further studies of correlated topological phenomena that do not have a single-particle counterpart.

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