PseudoGoldstone modes and dynamical gap generation from orderbythermaldisorder
Abstract
Accidental ground state degeneracies  those not a consequence of global symmetries of the Hamiltonian  are inevitably lifted by fluctuations, often leading to longrange order, a phenomenon known as "orderbydisorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for orderbythermaldisorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuationinduced pseudoGoldstone gap. We demonstrate this in a minimal twodimensional model that exhibits ObTD, the ferromagnetic Heisenbergcompass model on a square lattice. Using spindynamics simulations and selfconsistent meanfield calculations, we determine the pseudoGoldstone gap, $\Delta $, and show that at low temperatures it scales as the square root of temperature, $\sqrt{T} $. We establish that a powerlaw temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuationinduced free energy.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.11948
 arXiv:
 arXiv:2301.11948
 Bibcode:
 2023arXiv230111948K
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Main text: 7 pages and 3 figures. Supplemental material: 8 pages and 3 figures