Semiclassical evidence of columnar order in the fully frustrated transversefield Ising model on the square lattice
Abstract
We investigate the zerotemperature phase diagram of the fully frustrated transversefield Ising model on the square lattice both in the classical limit and in the presence of quantum fluctuations. At the classical level (the limit of infinite spin S ), we find that upon decreasing the transverse field Γ this model exhibits a phase transition from the fully polarized state into an eightfold degenerate translational symmetry breaking state. This phase can be identified to correspond to plaquette order in the dimer language and remains the lowestenergy state in the entire range of fields below the critical one, Γ_{c}. The eightfold degenerate solution that corresponds to columnar order in the dimer language is a saddle point of the classical energy. It is degenerate with the plaquette solution at Γ =0 and is only slightly higher in energy in the whole interval 0 <Γ <Γ_{c} . The effect of quantum fluctuations is investigated in the context of a large S expansion both for the plaquette and columnar structures. For this purpose we employ an approximate method allowing to estimate from above the fluctuationinduced correction to the energy of a configuration which at the classical level is a saddle point of the energy, not a local minimum, and find that the harmonic quantum fluctuations show a clear tendency to overcome the energy difference between the two states. For relatively high fields, the transition from the plaquette to the columnar state takes place at values of S large enough to be in the domain of validity of the harmonic approximation.
 Publication:

Physical Review B
 Pub Date:
 November 2014
 DOI:
 10.1103/PhysRevB.90.205109
 arXiv:
 arXiv:1408.3515
 Bibcode:
 2014PhRvB..90t5109C
 Keywords:

 05.50.+q;
 71.10.w;
 75.10.Jm;
 Lattice theory and statistics;
 Theories and models of manyelectron systems;
 Quantized spin models;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 14 pages, 6 figures