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Kaleidoscope of Exotic Quantum Phases in a Frustrated XY Model

Figure: Above: Antiferromagnetic arrangement of spins. Below: Arrangement of spins in a spin liquid, where there is no magnetic order. Author Galitski describes the spins as free ranging particle-like entities dubbed “spinons.” These spinons bob about, just as water molecules bob about in liquid water. (Image credit: E. Edwards)

PFC-supported research at JQI has uncovered evidence for a long-sought-after quantum state of matter, a spin liquid. You can’t pour a spin liquid into a glass.  It’s not a material at all, at least not a material you can touch. It is more like a kind of magnetic disorder within an ordered array of atoms.

Spin liquids arise due to “frustration,” a baffling condition wherein neighboring atom spins try to anti-align in up-down-up-down fashion, but are prevented from doing so by the intrinsic geometry of the lattice (here, a honeycomb). Understanding frustration and the different ways a collection of magnetically interacting spins can arrange themselves might help in designing new types of electronic circuitry.

One compromise that a frustrated spin system makes is to simultaneously exist in many spin orientations . The researchers uncovered a spin liquid when exploring frustration in materials with a hexagonal (six-sided) unit cell lattice. They calculated what happened when a batch of atoms interacted among themselves in an array of hexagons consisting of 30 sites, where the spins are free to swing about in a two-dimensional plane (this kind of approach is called an XY model).

They found a “kaleidoscope” of phases that represent the different lowest-energy states that are allowed given a range of magnetic interactions. One of these phases turns out to be a true quantum spin liquid having no order at all.  Here, the entire sample co-exists in millions of quantum states simultaneously.

Christopher N. Varney, Kai Sun, Victor Galitski, and Marcos Rigol
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