Related papers: Many-body Chern number from statistical correlatio…
Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful…
The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems…
In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the…
Integer and fractional Chern insulators exhibit a nonzero quantized anomalous Hall conductivity due to a spontaneous breaking of time reversal symmetry. To identify nontrivial topology in their time-reversal symmetric many-body spectra, we…
While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include…
We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body…
The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated…
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…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…
Multi-terminal topological devices are a new generation of electronic devices with quantized properties robust against imperfections. In magnetic topological insulators, dissipationless edge states give functional devices in zero magnetic…
This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum…
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…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological…