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Physics Letters A

Critical properties of spins with pair and triplet interactions on a triangular lattice

D. Imbro, Per Chr. Hemmer

Published Jun 1, 1976• 25 citations
Publisher
DOI
10.1016/0375-9601(76)90585-5

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Considers the usual Ising model with pair interactions between nearest-neighbour spins sigma on the triangular lattice. The author evaluates the correlation M 3 =( sigma 1 sigma 2 sigma 3 ), where sigma 1 , sigma 2 , sigma 3 are the three spins at the vertices of a triangular face. This can be thought of as an order parameter associated with a three-spin 'field'. It vanishes at and above T c , and has a critical exponent of 1 / 8 .

Journal of Physics A Mathematical and General•Nov 1, 1975•18 citations
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.
We compute the properties of singlet and triplet bipolarons on two-dimensional lattices using the continuous-time quantum Monte Carlo algorithm. Properties of the bipolaron including the total energy, inverse mass, bipolaron radius, and number of phonons associated with the bipolaron demonstrate the qualitative difference between models of electron-phonon interaction with long-range interaction (screened Fr\"ohlich) and those with purely local (Holstein) interaction. A major result of our survey of the parameter space is the existence of extra-light hybrid singlet bipolarons consisting of an on-site and an off-site component on both square and triangular lattices. We also compute triplet properties of the bipolarons and the pair dispersion. For pair momenta on the edge of the Brillouin zone of the triangular lattice, we find that triplet states are more stable than singlets.