One of the main activities in modern condensed matter physics is the search for novel quantum states of matter, which do not have a classical counterpart. Highly frustrated magnetic materials provide a natural test bed for exploring these phases. Although elusive for many years, exotic quantum states of matter are slowly appearing in a number of frustrated spin Hamiltonians. Several types of exotic phases, including topological states, such as the time-reversal invariant Z
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spin liquid, double-semion spin liquids, Dirac spin liquids, and chiral spin liquids, have been proposed to exist in frustrated quantum magnets. The number keeps increasing as result of intense theoretical efforts in an attempt of identifying and solving simple models for frustrated quantum magnets. Unfortunately, in most cases these models are somewhat artificial and it remains unclear how to find experimental realizations.

The purpose of this seminar is to show that quantum spin liquids, which only break discrete symmetries, such as chiral or nematic liquids, could appear under quite general conditions near a quantum phase transition between a quantum paramagnet and a magnetically ordered state. A necessary condition is that the magnetic ordering must break both continuous and discrete symmetries of the underlying model. Like in the case of classical phase transitions in three spatial dimensions, the quantum phase transition in 2+1 dimensions can happen in two steps, leading to the stabilization of an intermediate spin liquid phase, which only breaks discrete symmetries of the original model. This phenomenon can be exploited as a guiding principle in the ongoing experimental search for quantum spin liquid phases.