arXiv subjects

Yu Yi-Xiang

Publications and source records attributed to Yu Yi-Xiang.

7 recordsLinked to original sources

arXiv2021

A new universal ratio in Random Matrix Theory and chaotic to integrable transition in Type-I and Type-II hybrid Sachdev-Ye-Kitaev models

We investigate chaotic to integrable transition 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. For the Majorana fermion case, we discuss both $ N $ even and $ N $ odd case. We make exact symmetry analysis on the possible symmetry class of both types of hybrid SYK in the 10 fold way by Random Matrix Theory (RMT) and also work out the degeneracy of each energy levels. We introduce a new universal ratio which is the ratio of the next nearest neighbour (NNN) energy level spacing to characterize the RMT. We perform exact diagonalization to evaluate both the known NN ratio and the new NNN ratio, then use both ratios to study Chaotic to Integrable transitions (CIT) in both types of hybrid SYK models. Some preliminary results on possible quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem and its dual version in the quantum chaotic side are given. We explore some intrinsic connections between the two complementary approaches to quantum chaos: the RMT and the Lyapunov exponent by the $ 1/N $ expansion in the large $ N $ limit at a suitable temperature range. Comments on some previously related works are given. Some future perspectives, especially the failure of the Zamoloddchikov's c-theorem in 1d CFT RG flow are outlined.

cond-mat.str-el↗

arXiv2019

Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models

The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first introduced by Gross and Rosenhaus. Here we focus on the 2-colored case and 4-colored case with balanced number of Majorana fermion $N$. By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant anti-unitary and unitary operators, we show that the color degree of freedoms lead to novel quantum chaotic behaviours. When $N$ is odd, different symmetry operators need to be constructed to make the classifications complete. The 2-colored case only show 3-fold Wigner-Dyson way, and the 4-colored case show 10-fold generalized Wigner-Dyson way which may also have non-trivial edge exponents. We also study 2- and 4-colored hybrid SYK models which display many salient quantum chaotic features hidden in the corresponding pure SYK models. These features motivate us to develop a systematic RMT to study the energy level statistics of 2 or 4 un-correlated random matrix ensembles. The exact diagonalizations are performed to study both the bulk energy level statistics and the edge exponents and find excellent agreements with our exact maximal symmetry classifications. Our complete and systematic methods can be easily extended to study the generic imbalanced cases. They may be transferred to the classifications of colored tensor models, quantum chromodynamics with pairings across different colors, quantum black holes and interacting symmetry protected (or enriched) topological phases.

cond-mat.str-el↗

arXiv2017

High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice

Searching for the first topological superfluid (TSF) remains a primary goal of modern science. Here we study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling (SOC) in a normal Zeeman field. By imposing self-consistence equations at half filling, we find there are 3 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 multi-minima structure of the ground state energy landscape. There is a new class of topological phase transition 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 the two new 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 explore their spatial and spin structures. We find 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 also elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. Experimental implications in both 2d non-centrosymmetric materials under a periodic substrate and cold atoms in an optical lattice are given.

cond-mat.quant-gas↗

arXiv2016

Parity oscillations and photon correlation functions in the $ Z_2/U(1) $ Dicke model at a finite number of atoms or qubits

In this work, by using the strong coupling expansion and exact diagonization (ED), we study the $ Z_2/U(1) $ Dicke model with independent rotating wave (RW) coupling $ g $ and counter-rotating wave (CRW) coupling $ g^{\prime} $ at a finite $ N $. This model includes the four standard quantum optics model: Rabi, Dicke, Jaynes-Cummings ( JC ) and Tavis-Cummings (TC) model as its various special limits. We show that in the super-radiant phase, the system's energy levels are grouped into doublets with even and odd parity. Any anisotropy $ β=g/g^{\prime} \neq 1 $ leads to the oscillation of parities in both the ground and excited doublets as the atom-photon coupling strength increases. The oscillations will be pushed to the infinite coupling strength in the isotropic $ Z_2 $ limit $ β=1 $. We find nearly perfect agreements between the strong coupling expansion and the ED in the super-radiant regime. We also compute the photon correlation functions, squeezing spectrum, number correlation functions which can be measured by various standard optical techniques.

cond-mat.quant-gas↗

arXiv2015

Photon Berry phases, Instantons, Schrodinger Cats with oscillating parities and crossover from $ U(1) $ to $ Z_2 $ limit in cavity QED systems

In this work, we study the $ U(1)/Z_2 $ Dicke model at a finite $ N $ by using the $ 1/J $ expansion and exact diagonization. This model includes the four standard quantum optics model as its various special limits. The $ 1/J $ expansions is complementary to the strong coupling expansion used by the authors in arXiv:1512.08581 to study the same model in its dual $ Z_2/U(1) $ representation. We identify 3 regimes of the system's energy levels: the normal, $ U(1) $ and quantum tunneling (QT) regime. The system's energy levels are grouped into doublets which consist of scattering states and Schrodinger Cats with even ( e ) and odd ( o ) parities in the $ U(1) $ and quantum tunneling (QT) regime respectively. In the QT regime, by the WKB method, we find the emergencies of bound states one by one as the interaction strength increases, then investigate a new class of quantum tunneling processes through the instantons between the two bound states in the compact photon phase. It is the Berry phase interference effects in the instanton tunneling event which leads to Schrodinger Cats oscillating with even and odd parities in both ground and higher energy bound states. We map out the energy level evolution from the $ U(1) $ to the QT regime and also discuss some duality relations between the energy levels in the two regimes. We also compute the photon correlation functions, squeezing spectrum, number correlation functions in both regimes which can be measured by various experimental techniques. The combinations of the results achieved here by $ 1/J $ expansion and those in arXiv:1512.08581 by strong coupling method lead to rather complete understandings of the $ U(1)/Z_2 $ Dicke model at a finite $ N $ and any anisotropy parameter $ β$.

physics.atom-ph↗

arXiv2015

Comments on "Controlling Discrete and Continuous Symmetries in Superradiant Phase Transitions with Circuit QED Systems "

Recently, the authors of the commented PRL presented the $ N=\infty $ solution of the $ U(1)/Z_2 $ Dicke model studied by us previously. Here we point out that (1) The authors missed an important transformation relating the two parameter regimes, so their separate discussions on the two regimes is redundant. (2) Both $ N=\infty $ classical limit and $ 1/N $ quantum fluctuations have been achieved in two of our previously published papers. It is the $ 1/N $ quantum fluctuations which lead to the non-trivial new quantum phenomena. In view of only a few $ N=2\sim 9 $ qubits inside a circuit QED microwave cavity, they can be tested in near future experiments. (3) Several possible experimental implementations of the $ U(1)/Z_2 $ Dicke model have been proposed before and recently experimentally realized.

cond-mat.str-el↗

arXiv2011

Tuning the Tricritical Point with Spin-orbit Coupling in Polarized Fermionic Condensates

We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large varieties of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward regime of low temperature, high magnetic field, and high polarization as the SOC increases.

cond-mat.quant-gas↗