相关论文: Topological invariant of periodic many body wavefu…

Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer…

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk…

Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We…

Lattice models forming bands with higher Chern number offer an intriguing possibility for new phases of matter with no analogue in continuum Landau levels. Here, we establish the existence of a number of new bulk insulating states at…

Pauli's exclusion principle forces fermions to occupy distinct quantum states, creating a filled region of momentum space at low temperature, the Fermi sea, whose topology governs the system's response to perturbations and the nature of its…

The high-Chern number phases with a Chern number C>1 have been observed in a recent experiment that performed on the topological insulator (TI) multilayer structures, consisting of the alternating magnetic-doped and undoped TI layers. In…

We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single particle wave functions. For example, we construct the many-body…

Quench dynamics of topological phases have been studied in the past few years and dynamical topological invariants are formulated in different ways. Yet most of these invariants are limited to minimal systems in which Hamiltonians are…

We study a non-Hermitian Rice-Mele model without breaking time-reversal symmetry, with the non-Hermiticity arising from imbalanced hopping rates. The Berry connection, Berry curvature and Chern number are introduced in the context of…

In quantum many-body systems, characterizing topological phase transitions typically requires complex many-body topological invariants, which are costly to compute and measure. Inspired by quantum reservoir computing, we propose an…

We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks---a class of…

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…

Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…

The synthetic Floquet lattice, generated by multiple strong drives with mutually incommensurate frequencies, provides a powerful platform for the quantum simulation of topological phenomena. In this study, we propose a 4-band tight-binding…

In this thesis, we study chiral topological phases of 2+1 dimensional quantum matter. Such phases are abstractly characterized by their non-vanishing chiral central charge $c$, a topological invariant which appears as the coefficient of a…

We address the problem of identifying a 2+1d topologically ordered phase using measurements on the ground-state wavefunction. For non-chiral topological order, we describe a series of bulk multipartite entanglement measures that extract the…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict…

The energy and entanglement spectrum of fractionally filled interacting topological insulators exhibit a peculiar manifold of low energy states separated by a gap from a high energy set of spurious states. In the current manuscript, we show…

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The…