Showing papers by "Jinwu Ye published in 2018"

Two indices Sachdev-Ye-Kitaev model

Abstract: We study the original Sachdev-Ye (SY) model in its Majorana fermion representation which can be called the two indices Sachdev-Ye-Kitaev (SYK) model Its advantage over the original SY model in the $ SU(M) $ complex fermion representation is that it need no local constraints, so a $1/M $ expansion can be more easily performed Its advantage over the 4 indices SYK model is that it has only two site indices $ J_{ij} $ instead of four indices $ J_{ijkl} $, so it may fit the bulk string theory better By performing a $1/M $ expansion at $ N=\infty $, we show that a quantum spin liquid (QSL) state remains stable at a finite $ M $ The $ 1/M $ corrections are exactly marginal, so the system remains conformably invariant at any finite $ M $ The 4-point out of time correlation ( OTOC ) shows quantum chaos neither at $ N=\infty $ at any finite $ M $, nor at $ M=\infty $ at any finite $ N $ By looking at the replica off-diagonal channel, we find there is a quantum spin glass (QSG) instability at an exponentially suppressed temperature in $ M $ We work out a criterion for the two large numbers $ N $ and $ M $ to satisfy so that the QSG instability may be avoided We speculate that at any finite $ N $, the quantum chaos appears at the order of $ 1/M^{0} $, which is the subleading order in the $ 1/M $ expansion When the $ 1/N $ quantum fluctuations at any finite $ M $ are considered, from a general reparametrization symmetry breaking point of view, we argue that the eThis work may motivate future works to study the possible new gravity dual of the 2 indices SYK modelffective action should still be described by the Schwarzian one, the OTOC shows maximal quantum chaos

Class of topological phase transitions of Rashba spin-orbit coupled fermions on a square lattice

Abstract: We study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling in a normal Zeeman field. By imposing self-consistence equations at half filling with zero chemical potential, we find that there are three phases: band insulator (BI), superfluid (SF), and topological superfluid (TSF) with a Chern number $C=2$. The $C=2$ TSF happens in small Zeeman fields and weak interactions which is in the experimentally most easily accessible regime. The transition from the BI to the SF is a first-order one due to the multiminima structure of the ground state energy landscape. There is a class of topological phase transitions (TPTs) from the SF to the $C=2$ TSF at the low critical field ${h}_{c1}$, then another one from the $C=2$ TSF to the BI at the upper critical field ${h}_{c2}$. We derive effective actions to describe these two classes of topological phase transitions, then use them to study the Majorana edge modes and the zero modes inside the vortex core of the $C=2$ TSF near both ${h}_{c1}$ and ${h}_{c2}$, especially exploring their spatial and spin structures. We find that the edge modes decay into the bulk with oscillating behaviors and determine both the decay and oscillating lengths. We compute the bulk spectra and map out the Berry curvature distribution in momentum space near both ${h}_{c1}$ and ${h}_{c2}$. We elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. We also discuss the competitions between SFs and charge density wave states in more general cases. A possible classification scheme of all the TPTs in a square lattice is outlined. Comparisons with previous works on related systems are discussed. Possible experimental implications in cold atoms in an optical lattice are given.

Random matrices and quantum analog of Kolmogorov-Arnold-Moser theorem in hybrid Sachdev-Ye-Kitaev models

Abstract: Here we investigate possible quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem in two types of hybrid SYK models which contain both $ q=4 $ SYK with interaction $ J $ and $ q=2 $ SYK with an interaction $ K $ in Type I or $ (q=2)^2 $ SYK with an interaction $ \sqrt{K} $ in Type II . These models include hybrid Majorana fermion, complex fermion and bosonic SYK. We first introduce a new universal ratio which is the ratio of the next nearest neighbour (NNN) energy level spacing to characterize the random matrix behaviours. We make exact symmetry analysis on the possible symmetry class of both types of hybrid SYK in the 10 fold way and also work out the degeneracy of each energy levels. We perform exact diagonalization to evaluate both the known NN ratio and the new NNN ratio. In Type I, as $ K/J $ changes, there is always a chaotic to non-chaotic transition (CNCT) from the GUE to Poisson in all the hybrid fermionic SYK models, but not the hybrid bosonic SYK model. In Type II, there are always CNCT from the corresponding GOE, GUE or GSE dictated by the symmetry of the $ q=4 $ SYK to the Poisson dictated by $ ( q=2 )^2 $ SYK. When the double degeneracy at the $ q=4 $ ( or $ (q=2)^2 $ ) side is broken by the $ q=2 $ ( or $ q=4 $ ) perturbation in Type I ( or Type II), the new NNN ratio can be most effectively to quantify the stability of quantum chaos ( or the KAM ). We compare the stability of quantum chaos and KAM theorem near the integrability in all these hybrid SYK models. We also discuss some possible connections between CNCT characterized by the random matrix theory and the quantum phase transitions (QPT) characterized by renormalization groups. Quantum chaos in both types of hybrid SYK models are also contrasted with that in the $ U(1)/Z_2 $ Dicke model in quantum optics.