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In some low dimensional quantum spin systems, magnetization plateau is observed before the saturation in magnetization curve. enter image description here.

I have couple of questions related to this effect-

  1. It seems, magnetization plateau is called a entangled state, if so, how ?
  2. What could be the physical application of phenomena of magnetization plateau ?
  3. How observance of plateau is associated with breaking of some symmetry in the spin system (I think it is transnational).

It will be kind and great if somebody can comment or answer these queries .

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  1. It seems, magnetization plateau is called a entangled state, if so, how ?

That is at best an imprecise statement. As discussed in the "Magnetization Plateaus" chapter by Takigawa, M. and Mila, F. in the book Lacroix, C., Mendels, P., Mila, F. (eds) Introduction to Frustrated Magnetism, Springer (2010) there are different mechanisms that can generate magnetization plateaus. The most well-studied is related to order-by-disorder, in which a long-ranged classical state is stabilized by thermal or quantum fluctuations. This would be a product state, without entanglement. However, the literature also points out "quantum plateaus", in which quantum states are stabilized. These can be entangled.

Note that you can have both unentangled and entangled plateaus within the same system; see for example Nishimoto, S., Shibata, N. and Hotta, C., Nat. Commun. 4, 2287 (2013) discussing the kagome Heisenberg antiferromagnet. Their numerical results indicate that the $1/9$ plateau is a state with finite topological entanglement entropy. However, the nature of this state is still under debate; see Fang, D-z., Xi, N., Ran, S-J. and Su, G. Phys. Rev. B 107, L220401 (2023) arguing that the entanglement entropy in the state follows the critical scaling of a $c=1$ conformal field theory. Either scenario indicates a state with nontrivial entanglement properties.

  1. What could be the physical application of phenomena of magnetization plateau ?

I'm not aware of any specific proposed technological applications. In principle, robust plateaus may be exploitable in future devices (c.f. quantum Hall effects). For now, I would consider the phenomenon largely of basic scientific interest. If specific plateaus can realize interesting topological phases, perhaps these would be more robust to chemical disorder than zero-field realizations of the same phases.

  1. How observance of plateau is associated with breaking of some symmetry in the spin system (I think it is transnational).

Magnetization plateaus can be observed in systems both with and without translational symmetry breaking. For example, the $1/3$ plateau in triangular lattices breaks the translational symmetry of the crystal as its magnetic unit cell involves three sites rather than one, but the $1/2$ plateau in bond-alternating chains does not as both the magnetic and conventional unit cells involve two sites. See table 10.1 in the book chapter linked above for more examples.

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    $\begingroup$ "the 1/9 plateau is an entangled state." -- What does "entangled state" mean in this context? Pretty much all states in many-body systems are entangled, I guess the question is rather whether one can understand it phenomenologically in a mean-field sense? $\endgroup$
    – Norbert Schuch
    Commented Dec 23, 2023 at 20:28
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    $\begingroup$ @NorbertSchuch I tried to keep it somewhat vague, because they argued that it's a state with finite topological entanglement entropy, but the more recent paper argues the state can be described with a $c=1$ CFT. Both types of states have somehow "interesting" entanglement properties. $\endgroup$
    – Anyon
    Commented Dec 23, 2023 at 20:39
  • $\begingroup$ @Anyon, Thanks, I am unable to understand that how it breaks the translational symmetry, can you suggest some simple example or literature where I can check $\endgroup$
    – Schrodinger
    Commented Dec 25, 2023 at 5:04
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    $\begingroup$ @explorer I'd suggest reading the book chapter I mentioned, and specifically the part about the $1/3$ plateau in the triangular lattice antiferromagnet. The classical ground state at zero field is the $120^\circ$ order, a three-sublattice order that breaks the translational symmetry. In the plateau, a phase with two spins parallel to the magnetic field and one spin antiparallel to it emerges, that again breaks the translational symmetry since the magnetic unit cell is larger than the crystalline unit cell. $\endgroup$
    – Anyon
    Commented Dec 25, 2023 at 16:07
  • $\begingroup$ @Anyon, thank you very much $\endgroup$
    – Schrodinger
    Commented Dec 27, 2023 at 8:14

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