Related papers: Gain-loss-induced non-Abelian Bloch braids

Gain-loss-induced non-Abelian Bloch braids

URL: http://arxiv.org/abs/2306.13056v2
Date: Thu, 21 Sep 2023 05:23:54 GMT
Title: Gain-loss-induced non-Abelian Bloch braids
Authors: B. Midya
Abstract summary: Braid phase transition occurs when the gain-loss is tuned across exceptional point degeneracy. The proposed theory is conducive to synthesizing exceptional materials for applications in topological computation and information processing.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Onsite gain-loss-induced topological braiding principle of non-Hermitian energy bands is theoretically formulated in multiband lattice models with Hermitian hopping amplitudes. Braid phase transition occurs when the gain-loss parameter is tuned across exceptional point degeneracy. Laboratory realizable effective-Hamiltonians are proposed to realize braid groups $\mathbb{B}_2$ and $\mathbb{B}_3$ of two and three bands, respectively. While $\mathbb{B}_2$ is trivially Abelian, the group $\mathbb{B}_3$ features non-Abelian braiding and energy permutation originating from the collective behavior of multiple exceptional points. Phase diagrams with respect to lattice parameters to realize braid group generators and their non-commutativity are shown. The proposed theory is conducive to synthesizing exceptional materials for applications in topological computation and information processing.

Related papers

Entanglement renormalization of fractonic anisotropic $\mathbb{Z}_N$ Laplacian models [4.68169911641046]
Gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. We investigate the anisotropic $mathbbZ_N$ Laplacian model which can describe a family of fracton phases defined on arbitrary graphs.
arXiv Detail & Related papers (2024-09-26T18:36:23Z)
Volichenko-type metasymmetry of braided Majorana qubits [0.0]
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits. Mixed-bracket Heisenberg-Lie algebras are introduced.
arXiv Detail & Related papers (2024-06-02T21:50:29Z)
Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems [0.0]
We define the twisted Gauss law operator and implement the twisted gauging of the finite group on the lattice. We show the twisted gauging is equivalent to the two-step procedure of first applying the SPT entangler and then untwisted gauging.
arXiv Detail & Related papers (2024-05-23T18:00:02Z)
$\mathbb{Z}_N$ lattice gauge theories with matter fields [0.0]
We study fermions and bosons in $mathbb Z_N$ lattice gauge theories. We present analytical arguments for the most important phases and estimates for phase boundaries of the model.
arXiv Detail & Related papers (2023-08-24T21:05:15Z)
Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
arXiv Detail & Related papers (2023-06-21T10:11:28Z)
Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
arXiv Detail & Related papers (2023-01-13T16:25:25Z)
Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
arXiv Detail & Related papers (2022-10-19T02:28:44Z)
Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces [52.424621227687894]
We introduce a unified framework for group equivariant networks on homogeneous spaces. We take advantage of the sparsity of Fourier coefficients of the lifted feature fields. We show that other methods treating features as the Fourier coefficients in the stabilizer subgroup are special cases of our activation.
arXiv Detail & Related papers (2022-06-16T17:59:01Z)
Multi-gap topology and non-Abelian braiding of phonons from first principles [5.138204888245502]
Non-Abelian states of matter can encode information immune from environmental noise. We show that phonons can carry non-Abelian frame charges at the band crossing points of their frequency spectrum. Our work provides a new quasiparticle platform for realizable non-Abelian braiding in reciprocal space.
arXiv Detail & Related papers (2021-11-10T19:00:04Z)
Quantum double aspects of surface code models [77.34726150561087]
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
arXiv Detail & Related papers (2021-06-25T17:03:38Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.