Related papers: Topological Order in Neural Wavefunctions
Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density…
The discovery of zero-field fractional Chern insulators (FCIs) in moir\'e materials has attracted intense interest in the interplay between topology and correlations. Here, we demonstrate that fractionalized topological order can emerge…
A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a…
A local Hamiltonian with Topological Quantum Order (TQO) has a robust ground state degeneracy that makes it an excellent quantum memory candidate. This memory can be corrupted however if part of the state leaves the protected ground state…
We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…
Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…
One of the most profound features of topologically ordered states of matter, such as the fractional quantum Hall (FQH) states, is that they possess topology-dependent ground state degeneracies that are robust to all local perturbations.…
We present a class of states with both topological and conventional Landau order that arise out of strongly interacting spinless fermions in fractionally filled and topologically non-trivial bands with Chern number $C=\pm 1$. These quantum…
This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…
The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered…
Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
Fascination in topological materials originates from their remarkable response properties and exotic quasiparticles which can be utilized in quantum technologies. In particular, large-scale efforts are currently focused on realizing…
There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. ``Interpretability'' remains a concern: can we understand…