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The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few…

At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered…

Recent experiments on the "hyper-kagome" lattice system Na$_4$Ir$_3$O$_8$ have demonstrated that it is a rare example of a three dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary…

Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as…

One of the key questions concerning frustrated lattices that has lately emerged is the role of disorder in inducing spin-liquid-like properties. In this context, the quantum kagome antiferromagnets YCu$_3$(OH)$_6$Cl$_3$, which has been…

Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-$1$ model on the square lattice with the nearest-neighbor bilinear ($J_1$) and biquadratic ($K_1$) interactions. We…

We review the interplay of frustration and strong electronic correlations in quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases…

A new type of magnetically frustrated lattice is found in the layered fluoride NaBa2Mn3F11. A kagome-type array of regular triangles composed of Mn2+ ions (spin 5/2) deforms so as to generate the next-nearest-neighbor interaction J2 between…

Frustration, spin correlations and interplay between competing degrees of freedom are some of the key ingredients that underlie exotic states with fractional excitations in quantum materials. Rare-earth based two dimensional magnetic…

Quantum simulators based on cold atomic gases can provide an ideal platform to study the microscopic mechanisms behind intriguing properties of solid materials and further explore novel exotic phenomena inaccessible by chemical synthesis.…

The three-dimensional (3D) magnet KBaFe$_2$(PO$_4$)$_3$ hosts a double-trillium lattice of Fe$^{3+}$ (spin, $S=5/2$) ions offering a prototypical platform to study the frustration induced effects in 3D. Through magnetization, specific heat,…

Geometrically frustrated many-particle quantum systems are notoriously hard to study numerically but are of profound interest because of their unusual properties and emergent phenomena. In these systems energetic constraints cannot be…

The Kagome-lattice-based material, Volborthite, $\mathrm{Cu_3 V_2 O_7 (OH)_2 \cdot 2 H_2 O}$, has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interactions. Here…

The search for two dimensional quantum spin liquids, exotic magnetic states with an entangled ground state remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism during the last decades. Recently,…

Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range…

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of…

Excitations which carry "fractional" quantum numbers are known to exist in one dimension in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. Fractional excitations have also been invoked to explain the breakdown…

The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S=1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was…

Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter, however, even…

The three-dimensional frustrated spin lattice in MgCrGaO4, where Cr3+ ions occupy a pyrochlore-like network, exemplifies a quantum magnet with competing interactions, macroscopic degeneracy, and exotic low-energy excitations. Using…