Sachdev–Ye–Kitaev model
In condensed matter physics and black hole physics, the Sachdev–Ye–Kitaev (SYK) model commonly known as SYK model is an exactly solvable model initially proposed by Subir Sachdev and Jinwu Ye,[1] and later modified by Alexei Kitaev to the present commonly used form.[2][3] The model is believed to bring insights into the understanding of strongly correlated materials and it also has a close relation with the discrete model of AdS/CFT, and fermionic code. Many condensed matter systems, such as quantum dot coupled to topological superconducting wires[4], graphene flake with irregular boundary[5], and kagome optical lattice with impurities [6], are proposed to be modeled by it. Some variants of the model is amenable to digital quantum simulation,[7] with pioneering experiments implemented in a NMR setting.[8]
SYK model
Let be an integer and an even integer such that , consider a set of Majorana Fermions which are Fermion operators satisfying conditions: (1) Hermitian ; (2) Clifford relation . Choosing a random variable such that the expectation satisfy: (1) ; and (2) , Then the SYK model is defined as
.
Note that sometimes, an extra normalization factor will be added.
The more famous model is when , then the model becomes
,
notice that here the factor is added for coincidence with the usually used form.
See also
References
- ^ Sachdev, Subir; Ye, Jinwu (1993-05-24). "Gapless spin-fluid ground state in a random quantum Heisenberg magnet". Physical Review Letters. 70 (21): 3339–3342. arXiv:cond-mat/9212030. Bibcode:1993PhRvL..70.3339S. doi:10.1103/PhysRevLett.70.3339. PMID 10053843.
- ^ "Alexei Kitaev, Caltech & KITP, A simple model of quantum holography (part 1)". online.kitp.ucsb.edu. Retrieved 2019-11-02.
- ^ "Alexei Kitaev, Caltech, A simple model of quantum holography (part 2)". online.kitp.ucsb.edu. Retrieved 2019-11-02.
- ^ Chew, Aaron; Essin, Andrew; Alicea, Jason (2017-09-29). "Approximating the Sachdev-Ye-Kitaev model with Majorana wires". Phys. Rev. B. 96 (12): 121119. doi:10.1103/PhysRevB.96.121119.
- ^ Chen, Anffany; Ilan, R.; Juan, F.; Pikulin, D.I.; Franz, M. (2018-06-18). "Quantum Holography in a Graphene Flake with an Irregular Boundary". Phys. Rev. Lett. 121 (3): 036403. doi:10.1103/PhysRevLett.121.036403.
- ^ Wei, Chenan; Sedrakyan, Tigran (2021-01-29). "Optical lattice platform for the Sachdev-Ye-Kitaev model". Phys. Rev. A. 103 (1): 013323. arXiv:2005.07640. Bibcode:2021PhRvA.103a3323W. doi:10.1103/PhysRevA.103.013323.
- ^ García-Álvarez, L.; Egusquiza, I.L.; Lamata, L.; del Campo, A.; Sonner, J.; Solano, E. (2017). "Digital Quantum Simulation of Minimal AdS/CFT". Physical Review Letters. 119: 040501. arXiv:1607.08560. Bibcode:2017PhRvL.119d0501G. doi:10.1103/PhysRevLett.119.040501.
- ^ Luo, Z.; You, Y.-Z.; Li, J.; Jian, C.-M.; Lu, D.; Xu, C.; Zeng, B.; Laflamme, R. (2019). "Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-Kitaev model". npj Quantum Information. 5: 53. arXiv:1712.06458. Bibcode:2019npjQI...5...53L. doi:10.1038/s41534-019-0166-7.