scholarly journals Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice

2019 ◽  
Vol 99 (5) ◽  
Author(s):  
C. B. Larsen ◽  
A. T. Rømer ◽  
S. Janas ◽  
F. Treue ◽  
B. Mønsted ◽  
...  
Keyword(s):  
Exact Diagonalization ◽  
Exchange Model ◽  
Square Lattice ◽  
Ring Exchange

scholarly journals Spin wave theory of spin-1/2 XY model with ring exchange on a triangular lattice

2013 ◽  
Vol 91 (7) ◽  
pp. 542-547 ◽  
Author(s):  
Solomon A. Owerre
Keyword(s):  
Phase Transition ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Finite Temperature ◽  
Wave Theory ◽  
Square Lattice ◽  
Xy Model ◽  
Superfluid Phase ◽  
Zero Temperature ◽  
Ring Exchange

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.

Sign in / Sign up

Export Citation Format

Share Document