There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

Floquet engineering is the concept of tailoring a system by a periodic drive, and it is
increasingly employed in many areas of physics. Ultracold atoms in optical lattices offer a …

The interplay between spontaneous symmetry breaking and topology can result in exotic
quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state …

The discovery of the quantum spin Hall effect and topological insulators more than a decade
ago has revolutionized modern condensed matter physics. Today, the field of topological …

The “sign problem”(SP) is a fundamental limitation to simulations of strongly correlated
matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians …

We present a theory of the superfluid weight in multiband attractive Hubbard models within
the Bardeen-Cooper-Schrieffer (BCS) mean-field framework. We show how to separate the …

While the recent advances in topology have led to a classification scheme for electronic
bands described by the standard theory of metals, a similar scheme has not emerged for …

While advances in electronic band theory have brought to light new topological systems,
understanding the interplay of band topology and electronic interactions remains a frontier …

The bulk–boundary correspondence, a fundamental principle relating the topological
invariants of the bulk to the presence of edge states, is modified in periodically driven …

The quantum geometry of Bloch states fundamentally affects a wide range of physical
phenomena. The quantum Hall effect, for example, is governed by the Chern number, and …