2023/09/10 by Qianqian Shi, Shi, Qian-Qian, Huan-Qiang Zhou +5
Physics and Astronomy · Earth and Planetary Sciences · #Theoretical and Computational Physics #Statistical Mechanics and Entropy #High-pressure geophysics and materials
paper · pdf · doi:10.48550/arxiv.2309.04973
It is found that the staggered \rm SU(4) ferromagnetic spin-orbital model accommodates highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes. The spontaneous symmetry breaking patterns are \rm SU(4) → \rm U(1) × \rm U(1) × \rm U(1), with three type-B Goldstone modes or \rm SO(4) ∼ \rm SU(2) × \rm SU(2) → \rm U(1) × \rm U(1), with two type-B Goldstone modes, depending on the system size being even or odd. An abstract fractal constitutes the underlying structure of the ground-state subspace. For a sequence of atypical degenerate ground states the fractal dimension is identified with the number of type-B Goldstone modes. This connection is established by evaluating the entanglement entropy for these atypical degenerate ground states. The observed universal finite system-size scaling behavior of the entanglement entropy follows a logarithmic scaling relation with the block size in the thermodynamic limit. In addition, the ground state degeneracies, depending on the boundary conditions adopted, constitute the two Fibonacci-Lucas sequences. In the limit of large system size their asymptotic forms become a self-similar logarithmic spiral. As a result, the model has a non-zero residual entropy Sr = -2 ln R , where R=( √(6)- √(2))/2.