Duality in the Sachdev-Ye-Kitaev Model

2018 ◽  
pp. 43-61 ◽  
Author(s):  
Sumit R. Das ◽  
Animik Ghosh ◽  
Antal Jevicki ◽  
Kenta Suzuki
Keyword(s):  
Kitaev Model

scholarly journals Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Antonio M. García-García ◽  
Yiyang Jia ◽  
Dario Rosa ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Quantum Chaos ◽  
Kitaev Model ◽  
Gravity Duals

scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

Topological phase boundary in a generalized Kitaev model

2016 ◽  
Vol 25 (5) ◽  
pp. 057101 ◽  
Author(s):  
Da-Ping Liu
Keyword(s):  
Phase Boundary ◽  
Topological Phase ◽  
Kitaev Model

scholarly journals Topological superconductivity in the Kondo-Kitaev model

2018 ◽  
Vol 98 (15) ◽  
Author(s):  
Wonjune Choi ◽  
Philipp W. Klein ◽  
Achim Rosch ◽  
Yong Baek Kim
Keyword(s):  
Kitaev Model ◽  
Topological Superconductivity

scholarly journals Sign-problem-free variant of the complex Sachdev-Ye-Kitaev model

2022 ◽  
Vol 105 (4) ◽  
Author(s):  
Byungmin Kang ◽  
Junggi Yoon
Keyword(s):  
Sign Problem ◽  
Kitaev Model

scholarly journals Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

2008 ◽  
Vol 78 (12) ◽  
Author(s):  
Sébastien Dusuel ◽  
Kai Phillip Schmidt ◽  
Julien Vidal ◽  
Rosa Letizia Zaffino
Keyword(s):  
Symmetry Breaking ◽  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Kitaev Model

scholarly journals Spin wave theory of a one-dimensional generalized Kitaev model

2020 ◽  
Vol 102 (13) ◽  
Author(s):  
Wang Yang ◽  
Alberto Nocera ◽  
Ian Affleck
Keyword(s):  
Spin Wave ◽  
Wave Theory ◽  
One Dimensional ◽  
Spin Wave Theory ◽  
Kitaev Model
Sign in / Sign up

Export Citation Format

Share Document