Entropy of entanglement and multifractal exponents for random states

Quantum computation of multifractal exponents through the quantum wavelet transform

We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant e.g. for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.

具有随机长程跳跃的受监测自由费米子中的纠缠转变与多重分形

Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping

研究具有随机幂律跳跃的一维受监测非相互作用复费米子链的纠缠动力学，通过分析不同α值下稳态纠缠熵的缩放情况，确定依赖于α的测量诱导相变，突出超扩散经典跳跃在纠缠动力学中的重要性及与传统纠缠源的区别。

Multifractality meets entanglement: relation for non-ergodic extended states

In this work we establish a relation between entanglement entropy and fractal dimension $D$ of generic many-body wave functions, by generalizing the result of Don N. Page [Phys. Rev. Lett. 71, 1291] to the case of {\it sparse} random pure states (S-RPS). These S-RPS living in a Hilbert space of size $N$ are defined as normalized vectors with only $N^D$ ($0 \le D \le 1$) random non-zero elements. For $D=1$ these states used by Page represent ergodic states at infinite temperature. However, for $0<D<1$ the S-RPS are non-ergodic and fractal as they are confined in a vanishing ratio $N^D/N$ of the…

Entanglement and localization of wavefunctions

We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.

Dynamical phases in a "multifractal" Rosenzweig-Porter model

We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the {\it averaged} survival probability may decay with time as the simple exponent, as the stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson model on Ran…

双空间不变性作为多标度临界态的通用判据

Dual-Space Invariance as a Universal Criterion for Multifractal Critical States

本文提出双空间不变性作为识别多标度临界态的通用判据，通过数值模拟展示其在位置和动量空间中的标度行为特征。