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In condensed matter physics, people always say quantum liquid or spin liquid. What does liquid mean?

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Usually "quantum liquid" refers to the ground state of a Hamiltonian that do not break translation symmetry of the Hamiltonian. (In a sense, "quantum gas" = "quantum liquid".) "Quantum spin liquid" refers to the ground state of a spin Hamiltonian that do not break spin-rotation and translation symmetries of the Hamiltonian.

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Historically, the terms gas, liquid and (crystalline) solid meant, respectively: weak/no interactions between particles, strong interactions but statistical translation/orientation invariance, and finally breaking of translation/orientation invariance. Applied to more spin systems, a liquid would have translational invariance, but some global order --- i.e. not disordered like a "gas". Of course, this term is not absolutely precise, and often practitioners will define their terms in talks and papers. You should treat them as descriptive rather than normative.

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Thanks, can you provide an example about the global order liqiud possesses and quantum liquid possesses, respectively? –  a0087946gy Oct 1 '12 at 13:50
    
The gas/liquid transition is usually characterised by density. In spin liquids, usually some form of spin ordering, e.g. algebraic decays of spin correlations. –  genneth Oct 1 '12 at 15:07
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gas = particles are so little packed that they can easily move.

liquid = particles are fairly dense packed but can move over long distances.

solid = particles are so densely packed that they are confined to small vibrations araound an equilibrium position (site), and larger moves (site changes) are quite rare. In many cases, the sites form a periodic lattice; then we have a crystal.

Between these phases are so-called phase transitions, that provide (in the thermodynamic limit) a clear dividing line.

The prefix ''quantum'' just means that the motion of the particles cannot be described by classical mechanics.

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What can 'motion' mean in quantum sense? –  a0087946gy Oct 1 '12 at 14:26
    
@a0087946gy: The Ehrenfest theorem gives a possible answer. en.wikipedia.org/wiki/Ehrenfest_theorem –  Arnold Neumaier Oct 1 '12 at 14:32
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