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Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…

Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of…

At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard…

Quantum spin liquids have been at the forefront of correlated electron research ever since their original proposal in 1973, and the realization that they belong to the broader class of intrinsic topological orders, along with the fractional…

This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the…

Spin liquids are a paradigmatic example of a non-trivial state of matter, and the search for new spin liquids is a key direction of physics, chemistry, and materials science. Geometric frustration -- where the geometry of the net that the…

In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…

Classical spin liquids have recently been analyzed in view of the single-gap homotopy classification of their dispersive eigenvectors. We show that the recent progress in defining multi-gap topologies, notably exemplified by the Euler…

Gauge theories are powerful tools in theoretical physics, allowing complex phenomena to be reduced to simple principles, and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming…

Quantum spin liquids are topological states of matter that arise in frustrated quantum magnets at low temperatures. At low energies, such states exhibit emergent gauge fields and fractionalized quasiparticles and can also possess enhanced…

Quantum spin liquids (QSLs) are long-range entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced…

Fracton emerges from strongly interacting many-body systems whose excitations, referred to as sub-dimensional particles, have restricted mobility or kinetic motions. These entities have garnered significant interest due to their…

We theoretically predict an exotic topological superfluid state with spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. This inhomogeneous topological superfluidity is induced by applying simultaneously a…

We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are…

We calculate the effect of the emergent photon on threshold production of spinons in $U(1)$ Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross-section dramatically,…

The search for quantum spin liquids (QSL) -- topological magnets with fractionalized excitations -- has been a central theme in condensed matter and materials physics. While theories are no longer in short supply, tracking down materials…

Quantum spin liquid (QSL) is an exotic quantum phase of matter whose ground state is quantum-mechanically entangled without any magnetic ordering. A central issue concerns emergent excitations that characterize QSLs, which are…

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of…

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…

On a lattice composed of triangular plaquettes where antiferromagnetic exchange interactions between localized spins cannot be simultaneously satisfied, the system becomes geometrically frustrated with magnetically disordered phases…