Graph-theory treatment of one-dimensional strongly repulsive fermions

@article{Decamp2020GraphtheoryTO,
  title={Graph-theory treatment of one-dimensional strongly repulsive fermions},
  author={Jean Decamp and Jiangbin Gong and Huanqian Loh and Christian Miniatura},
  journal={Physical Review Research},
  year={2020}
}
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to quantum simulation and quantum computation due to their computational complexity. In this article, we exploit spectral graph theory to completely characterize the symmetry properties of one-dimensional fermionic mixtures in the strong interaction limit. We also… 

Figures from this paper

Universal graph description for one-dimensional exchange models
We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely Cayley graphs of the permutation group. Their
Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit
Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L
Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space
Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable

References

SHOWING 1-10 OF 127 REFERENCES
Quantum physics in one dimension
1. Peculiarities of d=1 2. Bosonization 3. Luttinger liquids 4. Refinements 5. Microscopic methods 6. Spin 1/2 chains 7. Interacting fermions on a lattice 8. Coupled fermionic chains 9. Disordered
Combinatorica 20
  • 505
  • 2000
Phys
  • Rev. 125, 164
  • 1962
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
‘S’
  • P. Alam
  • Composites Engineering: An A–Z Guide
  • 2021
‘T’
  • P. Alam
  • Composites Engineering: An A–Z Guide
  • 2021
‘Z’
  • P. Alam
  • Composites Engineering: An A–Z Guide
  • 2021
Colloquium : Many-body localization, thermalization, and entanglement
Thermalizing quantum systems are conventionallydescribed by statistical mechanics at equilib-rium. However, not all systems fall into this category, with many-body localization providinga generic
Comb
  • J. Haladyn
  • Mathematics
    Duchamp, Aesthetics and Capitalism
  • 2019
For example, when playing the Pick–6 Lotto, we must choose six numbers from the group 1 – 42. Obviously, we cannot repeat numbers. But more importantly, the order does not matter. In other words, we
Defect-Free Assembly of 2D Clusters of More Than 100 Single-Atom Quantum Systems.
We demonstrate the defect-free assembly of versatile target patterns of up 111 neutral atoms, building on a 361-site subset of a micro-optical architecture that readily provides thousands of sites
...
1
2
3
4
5
...