Coherent and dissipative dynamics at quantum phase transitions

We study the multipartite entanglement of a quantum many-body system undergoing a quantum quench. We quantify the multipartite entanglement through the quantum Fisher information (QFI) density, and we are able to express it after a quench in terms of a generalised response function. For pure state initial conditions and in the thermodynamic limit, we can express the QFI as the fluctuations of an observable computed in the so-called diagonal ensemble. We apply the formalism to the dynamics of a quantum Ising chain, after a quench in the transverse field. In this model the asymptotic state is, in almost all cases, more than two-partite entangled. Moreover, starting from the ferromagnetic phase, we find a divergence of multipartite entanglement for small quenches closely connected to a corresponding divergence of the correlation length.

Multipartite entanglement after a quantum quench

We study the multipartite entanglement of a quantum many-body system undergoing a quantum quench. We quantify multipartite entanglement through the quantum Fisher information (QFI) density and we are able to express it after a quench in terms of a generalized response function. For pure state initial conditions and in the thermodynamic limit, we can express the QFI as the fluctuations of an observable computed in the so-called diagonal ensemble. We apply the formalism to the dynamics of a quantum Ising chain after a quench in the transverse field. In this model the asymptotic state is, in almost all cases, more than two-partite entangled. Moreover, starting from the ferromagnetic phase, we find a divergence of multipartite entanglement for small quenches closely connected to a corresponding divergence of the correlation length.

In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional $s$-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students -- both theorists and experimentalists -- seeking to familiarize themselves with some of the basic concepts in the field.

Majorana bound states in semiconducting nanostructures

The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.

/pdf/universal-finite-size-scaling-around-topological-quantum-2c6ie58s0d.pdf

Universal Finite-Size Scaling around Topological Quantum Phase Transitions

We consider a finite-size scaling function across a topological phase transition in one-dimensional models. For models of noninteracting fermions it was shown to be universal for all topological symmetry classes and markedly asymmetric between trivial and topological sides of the transition [T. Gulden, M. Janas, Y. Wang, and A. Kamenev, Phys. Rev. Lett. 116, 026402 (2016)]. Here we verify its universality for the topological transition between dimerized and Haldane phases in bilinear-biquadratic spin-1 chain. To this end we perform high-accuracy variational matrix product state simulations. We show that the scaling function, expressed in terms of $L/\ensuremath{\xi}$, where $L$ is the chain length and $\ensuremath{\xi}$ is the correlation length, coincides with that of three species of noninteracting massive Majorana fermions. The latter is known to be a proper description of the conformal critical theory with central charge $c=3/2$. We have shown that it still holds away from the conformal point, including the finite-size corrections. We have also observed peculiar differences between even- and odd-size chains, which may be fully accounted for by residual interactions of the edge states.

Finite-size scaling at a topological transition: Bilinear-biquadratic spin-1 chain

Nonlinear absorption and refraction of Cs3Cu2Br5 perovskite

Universal Finite-Size Scaling around Topological Quantum Phase Transitions.

We consider scaling of the entanglement entropy across a topological quantum phase transition for the Kitaev chain model. The change of the topology manifests itself in a subleading term, which scales as ${L}^{\ensuremath{-}1/\ensuremath{\alpha}}$ with the size of the subsystem $L$, here $\ensuremath{\alpha}$ is the R\'enyi index. This term reveals the scaling function ${h}_{\ensuremath{\alpha}}(L/\ensuremath{\xi})$, where $\ensuremath{\xi}$ is the correlation length, which is sensitive to the topological index. The scaling function ${h}_{\ensuremath{\alpha}}(L/\ensuremath{\xi})$ is independent of model parameters, suggesting some degree of its universality.

pdf/finite-size-scaling-of-entanglement-entropy-in-one-1jhun9yvcf.pdf

Finite-size scaling of entanglement entropy in one-dimensional topological models

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Yuting Wang

Author Tools

Chat about Author