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Phys Rev Lett. 2003 Jan 10;90(1):016803. Epub 2003 Jan 10.

Quantum orders in an exact soluble model.

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Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.


We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: H=16g Sum S(y)(i)S(x)(i + empty set x)S(y)(i + empty set x + empty set y)S(x)(i + empty set y). We show that the ground states for g < 0 and g > 0 have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at g = 0 represents a new kind of phase transition that changes quantum orders but not symmetry. Both the Z2A and Z2B states contain Z2 lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.

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