Related papers: Topological bound on structure factor
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…
We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…
We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q^4$ term in the static structure factor $S(q)$ at small $\vec{q}$. Bands that saturate this bound satisfy a condition similar to Laplace's…
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…
Conventional Chern insulators are two-dimensional periodic structures that support unidirectional edge states at the boundary, while the wave propagation in the bulk regions is forbidden. The number of unidirectional edge states is governed…
Recently, it has been shown how topological phases of matter with crystalline symmetry and $U(1)$ charge conservation can be partially characterized by a set of many-body invariants, the discrete shift $\mathscr{S}_{\text{o}}$ and electric…
Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show…
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…
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…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-\delta$ dimensions and finite in size in $\delta$ dimensions, is fundamentally different from that of…
Disorder is ubiquitous in quantum materials, and its interplay with topology can generate phases absent in the clean limit. Using the Haldane model as a minimal setting, we show that disorder not only shifts topological boundaries but also…
The structure factor is a useful observable for probing charge density correlations in real materials, and its long-wavelength behavior encapsulated by ``quantum weight'' has recently gained prominence in the study of quantum geometry and…
Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…
The stability of fractional Chern insulators is widely believed to be predicted by the resemblance of their single-particle spectra to Landau levels. We investigate the scope of this geometric stability hypothesis by analyzing the stability…
We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum…
Most fractional quantum Hall states have been traditionally identified within a single energy band, such as the lowest Landau level or topological flat band. As more particles are introduced, they inevitably populate higher energy bands.…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
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…