A one dimensional model showing a quantum phase transition based on a singular potential

Phase transition through the splitting of self-dual spectral singularity in optical potentials

We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked in the most of previous studies scenario of the phase transition (known as $PT$-symmetry breaking in systems obeying parity-time symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial r…

谱转变与新一族准周期量子行走中的奇异连续谱

Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks

本文提出了一种新的准周期量子行走模型，展示了其在谱分析中的奇异连续谱特性。

Symmetry-Breaking Transition and Spectral Singularity in Coupled $\mathcal{PT}$-Symmetric Quantum Potentials

We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum scatterers, and apply that theory to demonstrate that the spectral singularities and $\mathcal{PT}$-symmetric transitions of single scattering cells may be observed in coupled systems, at the same or distinct values of the critical parameters, depending on the connection modes under which the scattering objects are coupled. We analyse the influences of the connect…

Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions

Phase transitions at a finite (i.e. non-zero) temperature are typically dominated by classical correlations, in contrast to zero temperature transitions where quantum mechanics plays an essential role. Therefore, it is natural to ask if there are any signatures of a finite temperature phase transition in measures that are sensitive only to quantum correlations. Here we study one such measure, namely, entanglement negativity, across finite temperature phase transitions in several exactly solvable Hamiltonians and find that it is a singular function of temperature across the transition. As an as…

Experimental observation of time singularity in classical-to-quantum chaos transition

The emergence of chaotic phenomena in a quantum system has long been an elusive subject. Experimental progresses in this subject have become urgently needed in recent years, when considerable theoretical studies have unveiled the vital roles of chaos in a broad range of topics in quantum physics. Here, we report the first experimental observation of time singularity, that signals a classical-to-quantum chaos transition and finds its origin in the {\it sudden change} in system's memory behaviors. The time singularity observed is an analog of the "dynamical quantum phase transition" (DQPT) -- pr…

具有发散多体纠缠的动力学量子相变

Dynamical quantum phase transition with singular multipartite entanglement

本研究针对一维横场Ising模型的非平衡淬火动力学，发现一类以临界时刻多体纠缠发散为特征的新型动力学量子相变，明确其普适类与基态相变不同，揭示其源于激发态相长干涉的非平衡本质，并探讨了实验实现与量子计量应用。