Journal of Physics Conference Series

Low-temperature density matrix renormalization group study on spin-1/2 frustrated spin chains

Shigetoshi Sota, Takami Tohyama

Published Jan 1, 2010• 3 citations

Abstract

We study the temperature dependence of the dynamical correlation function of the vector spin chirality on spin-1/2 zigzag XY spin chains by using the low-temperature dynamical density matrix renormalization group that we have developed recently. At zero temperature, gapless and gapful excitations of the chiralily are confirmed for systems with and without the chiral order, respectively. At finite temperatures, we find in the gapful system a characteristic temperature where the low-energy dynamical chirality correlation changes dramatically. This is in contrast to the system with the order where the correlation changes smoothly with temperature.

DOI: 10.1088/1742-6596/200/1/012191

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Journal of Physics Conference Series

Low-temperature density matrix renormalization group study on spin-1/2 frustrated spin chains

Shigetoshi Sota, Takami Tohyama

Published Jan 1, 2010• 3 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/200/1/012191

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We study spin chirality for a spin-

\frac{1}{2}

zigzag

XY

chain at low temperature by applying a low-temperature density-matrix renormalization group technique. We calculate temperature dependence of dynamical and static correlations of the chirality. In a chiral phase, chiral long-range order at zero temperature disappears at finite temperature, consistent with the fact that there is no long-range order at finite temperature in one-dimensional systems with short-range interactions. In a dimer phase next to the chiral phase, we find an enhancement of static chiral correlation as well as spin correlation with increasing temperature. The enhancement corresponds to the increase in spectral weight inside a gap in the dynamical chiral-correlation function. This temperature-induced chiral correlation is a demonstration of the presence of a chiral state in excited states.

κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x

, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.

We calculate the vector spin chirality for

S=1/2

zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the

S=1/2

zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.