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Bulletin of the American Physical Society

Role of cyclic four-spin exchange in doped two-leg ladders

Guillaume Roux, Steve White, Didier Poilblanc, Sylvain Capponi, Andreas Martin Läuchli

Published Mar 21, 2005• 0 citations
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We investigate a two-leg Heisenberg spin ladder with cyclic four-spin exchange by exploiting a newly-developed tensor network algorithm. The algorithm allows to efficiently compute the ground-state fidelity per lattice site, which enables us to establish the ground-state phase diagram for quantum lattice many-body systems. The latter is based on the observation that, for an infinite-size system, any singularity on a ground-state fidelity surface characterizes a critical point, at which the system undergoes a phase transition. For the two-leg Heisenberg spin-1/2 ladder with cyclic four-spin exchange, six different phases are identified: the ferromagnetic phase, the rung singlet phase, the staggered dimer phase, the scalar chirality phase, the dominant vector chirality region, and the dominant collinear spin region. Our findings are in a good agreement with the previous studies from the exact diagonalization and the density-matrix renormalization group.
Effect of four-spin cyclic exchange on magnetism is studied in the two-leg S=1/2 ladder. We develop an exact spin-chirality duality transformation, under which the system is self-dual when the four-spin exchange J4 is half of the two-spin exchange. Using the density-matrix renormalization-group method and the duality relation, we find that the four-spin exchange makes the vector-chirality correlation dominant. A "chirality short-range resonating-valence-bond" phase is identified for the first time at large J4.
Using continuous unitary transformations (CUTs) we calculate the one-triplet gap for the antiferromagnetic S=12S=\frac{1}{2}S=21​ two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying an efficient extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.