arXiv subjects

Sizheng Cao

Publications and source records attributed to Sizheng Cao.

5 recordsLinked to original sources

arXiv2025

Symmetry restoration in a fast scrambling system

Entanglement asymmetry -- used here as a direct probe of symmetry restoration -- provides a sharp diagnostic of post-quench dynamics. We test this idea in the complex Sachdev--Ye--Kitaev model with a conserved U(1) charge. Using exact diagonalization, we track the joint evolution of entanglement entropy and entanglement asymmetry after quenches from charge-asymmetric product states. We find rapid volume-law entanglement growth consistent with the subsystem eigenstate thermalization hypothesis, accompanied by a concurrent decay of entanglement asymmetry to a late-time plateau set by finite-size effects: small subsystems display near-complete restoration, while residual cross-sector weight yields a finite plateau. Notably, we uncover a quantum Mpemba effect: states prepared further from symmetry relax faster and approach lower residual asymmetry; disorder in the couplings renders this behavior more robust and monotonic across parameters. We further derive a Pinsker-type lower bound that ties the decay of asymmetry to differences in subsystem purity, identifying dephasing between U(1) charge sectors as the operative mechanism. These results establish entanglement asymmetry as a sensitive probe of symmetry restoration and thermalization, clarifying finite-size limits in fast-scrambling, closed quantum systems.

cond-mat.str-el↗

arXiv2024

Thermodynamic and Real-time Dynamic Properties of Complex Sachdev-Ye-Kitaev Model

We study the complex Sachdev-Ye-Kitaev (cSYK) numerically and investigate thermodynamic behavior of cSYK model across varying chemical potentials. We discover that the cSYK model remarkably mirrors the first-order phase transition seen in the van der Waals-Maxwell system, culminating at a non-mean-field critical point with distinctively different critical exponents. We analyze in detail the similarity between the van der Waals phase transition and the cSYK model, and further explore the mechanism by which the chemical potential drives the phase transition in the system. Exact diagonalization for the cSYK model reveals the significant impact of chemical potential on energy distribution, with observable energy gaps in the gapped phase. Quantum chaos indicators, including spectral form factors, suggest more stable energy states in the neutral case. Real-time dynamics, analyzed via analytical continuation of Schwinger-Dyson equations, show rapid decay in the gapless phase and prolonged oscillation lifetimes in the gapped regime. Spectral functions imply a shift from a continuous to a discrete energy level distribution, emphasizing the critical role of chemical potential in shaping spectral properties.

hep-th↗

arXiv2024

Excitation Transmission through a non-Hermitian traversable wormhole

This study explores the intricate real-time dynamics of a non-Hermitian system composed of two interconnected Sachdev-Ye-Kitaev (SYK) models. A central finding reveals that an excitation initially localized in the right SYK subsystem can be efficiently transmitted to the left subsystem subsequent to the characteristic scrambling time, a phenomenon facilitated by the intrinsic non-Hermitian nature of the system. The defining hallmark of non-Hermiticity is manifest in the asymmetric conveyance of quantum states, with the non-Hermitian parameter functioning as a tunable knob that selectively amplifies or dampens propagation modes on either side. Despite this inherent directional bias in state transfer, the system sustains two distinct phases, analogously likened to black holes and wormholes.

hep-th↗

arXiv2023

Matching partition functions of deformed JT gravity and the cSYK model

Motivated by recent analogies between the large-$q$ cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the $(0+1)$-dimensional cSYK model, with that of a $(1+1)$-dimensional gravitational model. We focus on a model of deformed JT gravity, characterized by some unknown dilaton potential function and unknown dilaton-to-Maxwell field coupling. By finding the general solutions, we are able to find the Lagrangian which produces the same partition function and equation of state as that of the considered SYK model. We go beyond showing that the thermodynamics overlaps, by also showing that the Lyapunov exponents, characterizing the degree of chaos, overlap close to the second order phase transition. In the low temperature rescaled regime, there remains open questions about the Lyapunov exponents, given that our analysis ignores the black hole back action which can be large in this regime.

hep-th↗

arXiv2022

Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models

We show that a non-Hermitian two coupled Sachdev-Ye-Kitaev (SYK) model can provide thermodynamic structure equivalent to Hermitian two coupled SYK model. The energy spectrum, the entanglement degree of the ground states and the low energy effective action of this model are not influenced by the non-Hermiticity. The novel biorthogonal ground states demonstrates that two SYK sites, one of which can be in the ground state and the other in the Schwarzian excited state by tuning the non-Hermiticity. We find evidence that the free energy is independent of the non-Hermiticity.

hep-th↗