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

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
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

References

SHOWING 1-10 OF 134 REFERENCES
Strongly interacting confined quantum systems in one dimension.
TLDR
This work proves that 1D fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates.
Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
We show that strongly interacting multicomponent gases in one dimension realize an effective spin chain, offering an alternative simple scenario for the study of one-dimensional (1D) quantum
Magnetism in Strongly Interacting One-Dimensional Quantum Mixtures.
TLDR
It is demonstrated that systems containing only a few bosons are an ideal setting in which to realize the highly sought-after itinerant ferromagnetic phase.
Fermi gases in one dimension: From Bethe ansatz to experiments
This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas-the
One-dimensional mixtures of several ultracold atoms: a review.
TLDR
The recent advances on trapped Bose-Fermi mixtures are described, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions.
Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach
Detailed analysis of the system of four interacting ultra-cold fermions confined in a one-dimensional harmonic trap is performed. The analysis is done in the framework of a simple variational ansatz
Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under
Verification of universal relations in a strongly interacting Fermi gas.
TLDR
Experimental verification of the Tan relations in a strongly interacting gas of fermionic atoms is provided by measuring both the microscopic and macroscopic quantities in the same system.
Crossover between few and many fermions in a harmonic trap
The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact
Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap.
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong
...
1
2
3
4
5
...