XY ring exchange model with frustrated Ising coupling on the triangular lattice

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.

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

Physical Review B ◽

10.1103/physrevb.99.054432 ◽

2019 ◽

Vol 99 (5) ◽

Cited By ~ 3

Author(s):

C. B. Larsen ◽

A. T. Rømer ◽

S. Janas ◽

F. Treue ◽

B. Mønsted ◽

...

Keyword(s):

Exact Diagonalization ◽

Exchange Model ◽

Square Lattice ◽

Ring Exchange

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Double Exchange Model in Triangular Lattice Studied by Truncated Polynomial Expansion Method

Communications in Computational Physics ◽

10.4208/cicp.160410.240910a ◽

2011 ◽

Vol 10 (2) ◽

pp. 422-432 ◽

Cited By ~ 3

Author(s):

Gui-Ping Zhang

Keyword(s):

Triangular Lattice ◽

Finite Size ◽

Double Exchange ◽

Expansion Method ◽

Exchange Model ◽

Polynomial Expansion ◽

Finite Size Effect ◽

Spin Configuration ◽

Half Filling ◽

Polynomial Expansion Method

AbstractThe low temperature properties of double exchange model in triangular lattice are investigated via truncated polynomial expansion method (TPEM), which reduces the computational complexity and enables parallel computation. We found that for the half-filling case a stable 120° spin configuration phase occurs owing to the frustration of triangular lattice and is further stabilized by antiferromagnetic (AF) su-perexchange interaction, while a transition between a stable ferromagnetic (FM) phase and a unique flux phase with small finite-size effect is induced by AF superexchange interaction for the quarter-filling case.

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