My research lies at the interface of quantum information theory, quantum chaos, and high-energy physics, with a particular focus on uncovering deep connections between entanglement, randomness, and gravitational dynamics. A central theme of my work is to understand how quantum information-theoretic quantities—such as entanglement, correlation functions, and operator growth—encode universal features of chaotic many-body systems and holographic duality.
Across my publications, I have developed new conceptual frameworks and computational tools to relate spectral statistics, quantum correlations, and entanglement measures. These works collectively address fundamental questions: How does chaos emerge in quantum systems? What distinguishes randomness from genuine chaos? How can entanglement be quantified in experimentally accessible ways? My contributions can be grouped into three main directions:
Bridging spectral statistics and quantum chaos via OTOCs
Distinguishing randomness and chaos in qubit and SYK-type models
Developing entanglement measures via Bell inequalities and multipartite systems
We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field theory, there is an analogous result with the average taken over the tensor product of many copies of the Heisenberg group, one copy for each field mode. The resulting formula is expressed as a path integral over two fields, providing a promising approach to the computation of the spectral form factor. We develop the formula that we have obtained using a coherent state description from the JC model and also in the context of the large-$N$ limit of CFT and Yang-Mills theory from the large-$N$ matrix quantum mechanics.
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$ SYK$_2$ model at high temperatures that is absent in the $N=2$ SYK$_2$ model. Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system. To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small $N$ issues. Finally, we demonstrate numerically that expectation values of observables computed in a random quantum state at late times are equivalent to the expectation values computed in the thermal ensemble in a Gaussian random one-qubit model.
We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.
Entanglement entropy gives quantitative understanding to the entanglement. We use the decomposition of the Hilbert space to discuss the properties of Quantum Entanglement. Therefore, it is hard to define the reduced density matrix from a partial trace operation with different centers. The center commutes with all elements in the Hilbert space. The choice of centers corresponds to observation on an entangling surface. We discuss the decomposition of the Hilbert space for the strong subadditivity and other related inequalities. In the Hamiltonian formulation, it is easier to obtain symmetry structure. We consider massless p-form theory as an example. The massless p-form theory in ($2p+2$)-dimensions has global symmetry, similar to the electric-magnetic duality, connecting centers in the ground state. We find a duality structure in centers. It is hard to compute the entanglement entropy from the partial trace operation in Quantum Field Theory. We propose the Lagrangian formulation from the Hamiltonian formulation to compute the entanglement entropy with centers. From the Lagrangian method, the codimension two surface term in the Einstein gravity theory should correspond to a non-tensor product decomposition. Finally, we use the strong-coupling expansion to compute the entanglement entropy of the SU($N$) Yang-Mills lattice gauge theory in the fundamental representation from the extended lattice model. Our result shows a spatial area term when total dimensions are higher than two and $N>1$.