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Quantum spin liquid

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Quantum spin liquid

In condensed matter physics, quantum spin liquid is a state that can be achieved in a system of interacting quantum spins. The state is referred to as a "liquid" as it is a disordered state in comparison to a ferromagnetic spin state,[1] much in the way liquid water is in a disordered state compared to crystalline ice. However, unlike other disordered states, a quantum spin liquid state preserves its disorder to very low temperatures.[2]

The quantum spin liquid state was first proposed by physicist Phil Anderson in 1973 as the ground state for a system of spins on a triangular lattice that interact with their nearest neighbors via the so-called antiferromagnetic interaction. Quantum spin liquids generated further interest when in 1987 Anderson proposed a theory that described high temperature superconductivity in terms of a disordered spin-liquid state.[3] A quantum spin liquid state in κ-(BEDT-TTF)2Cu2(CN)3 was first thoroughly mapped using muon spin spectroscopy by a team led by Dr Francis Pratt at ISIS neutron source, UK in March, 2011.[4]

Examples

Several physical models have a disordered ground state that can be described as a quantum spin liquid.

Frustrated magnetic moments

Frustrated Ising spins on a triangle.

Localized spins are frustrated if there exist competing exchange interactions that can not all be satisfied at the same time, leading to a large degeneracy of the system's ground state. A triangle of Ising spins (meaning the only possible orientations of the spins are "up" and "down"), which interact antiferromagnetically, is a simple example for frustration. In the ground state, two of the spins can be antiparallel but the third one cannot. This leads to an increase of possible orientations (six in this case) of the spins in the ground state, enhancing fluctuations and thus suppressing magnetic ordering.

Some frustrated materials with different lattice structures and their Curie-Weiss temperature are listed in the table.[2] All of them are proposed spin liquid candidates.
Material Lattice \Theta _{cw} [K]
κ-(BEDT-TTF)2Cu2(CN)3 anisotropic triangular -375
ZnCu3(OH)6Cl2 (herbertsmithite) Kagome -241
BaCu3V2O8(OH)2 (vesignieite) Kagome
Na4Ir3O8 Hyperkagome -650
Cu-(1,3-benzenedicarboxylate) Kagome -33 [5]
Rb2Cu3SnF12 Kagome [6]

Resonating valence bonds (RVB)

Valence bond solid. The bonds form a specific pattern and consist of pairs of entangled spins.

To build a ground state without magnetic moment, valence bond states can be used, where two electron spins form a spin 0 singlet due to the antiferromagnetic interaction. If every spin in the system is bound like this, the state of the system as a whole has spin 0 too and is non-magnetic. The two spins forming the bond are maximally entangled, while not being entangled with the other spins. If all spins are distributed to certain localized static bonds, this is called a valence bond solid (VBS).

There are two things that still distinguish a VBS from a spin liquid: First, by ordering the bonds in a certain way, the lattice symmetry is usually broken, which is not the case for a spin liquid. Second, this ground state lacks long-range entanglement. To achieve this, quantum mechanical fluctuations of the valence bonds must be allowed, leading to a ground state consisting of a superposition of many different partitionings of spins into valence bonds. If the partitionings are equally distributed (with the same quantum amplitude), there is no preference for any specific partitioning ("valence bond liquid"). This kind of ground state wavefunction was proposed by P. W. Anderson in 1973 as the ground state of spin liquids[7] and is called a resonating valence bond (RVB) state. These states are of great theoretical interest as they are proposed to play a key role in high-temperature superconductor physics.[8]


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