scholarly journals Triangular lattice Majorana-Hubbard model: Mean-field theory and DMRG on a width-4 torus

2021 ◽  
Vol 103 (11) ◽  
Author(s):  
Tarun Tummuru ◽  
Alberto Nocera ◽  
Ian Affleck
Keyword(s):  
Field Theory ◽  
Hubbard Model ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field

COMPREHENSIVE MEAN FIELD THEORY FOR THE HUBBARD MODEL

1992 ◽  
Vol 06 (05n06) ◽  
pp. 731-747 ◽  
Author(s):  
V. JANIŠ ◽  
D. VOLLHARDT
Keyword(s):  
Field Theory ◽  
Energy Transfer ◽  
Hubbard Model ◽  
Entire Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Exact Expression ◽  
Grand Potential ◽  
Input Parameters

We derive an exact expression for the grand potential of the Hubbard model in d=∞ dimensions. By simplifying the energy transfer between up and down spins we obtain a comprehensive mean-field theory for this model. It is (i) thermodynamically consistent in the entire range of input parameters, (ii) conserving and, (iii) exact in several non-trivial limits, e. g. in the free (U→0), atomic (t→0) and Heisenberg (U≫t, n=1) limit.

Pinwheel and herringbone structures of planar rotors with anisotropic interactions on a triangular lattice with vacancies

1984 ◽  
Vol 62 (9) ◽  
pp. 915-934 ◽  
Author(s):  
A. B. Harris ◽  
O. G. Mouritsen ◽  
A. J. Berlinsky
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field ◽  
Wave Theory ◽  
Finite Domain ◽  
Unexpected Result ◽  
Spin Wave Theory

A variety of theoretical techniques, including Monte Carlo (MC), mean field theory, and spin-wave theory, are used to analyze the phase diagram of a system of planar rotors on a triangular lattice with vacancies. A simple anisotropic interaction, which mimics the electric quadrupole–quadrupole interaction for diatomic molecules confined to rotate in the plane of the surface, induces a herringbone-ordered structure for the pure (x = 1) system, whereas for x ≈ 0.75, if the vacancies are free to move, a 2 × 2 pinwheel structure is favored. For x = 0.75, MC calculations give a continuous transition with Ising exponents in agreement with renormalization group predictions for this universality class, the Heisenberg model with corner-type cubic anisotropy. Mean field theory gives the unexpected result that the pinwheel phase is stable only along the herringbone-disordered state coexistence line in the temperature versus chemical potential phase diagram. Spin-wave theory is used to show that there is, in fact, a finite domain of stability for the pinwheel phase, and a complete phase diagram, which encompasses all available information, is conjectured.

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