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Quantum phase transitions and topological orders in spin chains and ladders
No full textDimerized antiferromagnetic spin-1/2 chains and ladders demonstrate quantum critical
phase transition, the existence or absence of which is dependent on the dimerization
and the dimerization pattern of the chain and the ladder, respectively. The
gapped phases can not be distinguished by the conventional Landau long-range
order parameters. However, they possess non-local topological string order parameters
which can be used to classify different phases. We utilize the self-consistent
free fermionic approximation and some standard results for exactly solved models
to analytically calculate the string order parameters of dimerized spin chains. As a
complement parameter the gapped phases possess the topological number, called the
winding number and they are characterized by different integer values of the winding
number. In order to calculate the string order parameters and winding numbers
in dimerized spin chains and two-leg ladders we use analytical methods such as the
Jordan-Wigner transformation, mean-field approximation, duality transformations,
and some standard results available for the exactly 1D solve models. It is shown
that the winding number provides the complementary framework to the string order
parameter to characterize the topological gapped phases
