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• W2595498794 abstract "We apply imaginary-time evolution, ${rm e}^{-tau H}$, to study relaxation dynamics of gapless quantum antiferromagnets described by the spin-rotation invariant Heisenberg Hamiltonian ($H$). Using quantum Monte Carlo simulations, we propagate an initial state with maximal order parameter $m^z_s$ (the staggered magnetization) in the $z$ spin direction and monitor the expectation value $langle m^z_srangle $ as a function of the time $tau$. Different system sizes of lengths $L$ exhibit an initial size-independent relaxation of $langle m^z_srangle$ toward its value the spontaneously symmetry-broken state, followed by a size-dependent final decay to zero. We develop a generic finite-size scaling theory which shows that the relaxation time diverges asymptotically as $L^z$ where $z$ is the dynamic exponent of the low energy excitations. We use the scaling theory to develop a way of extracting the dynamic exponent from the numerical finite-size data. We apply the method to spin-$1/2$ Heisenberg antiferromagnets on two different lattice geometries; the two-dimensional (2D) square lattice as well as a site-diluted square lattice at the percolation threshold. In the 2D case we obtain $z=2.001(5)$, which is consistent with the known value $z=2$, while for the site-dilutes lattice we find $z=3.90(1)$. This is an improvement on previous estimates of $zapprox 3.7$. The scaling results also show a fundamental difference between the two cases: In the 2D system the data can be collapsed onto a common scaling function even when $langle m^z_srangle$ is relatively large, reflecting the Anderson tower of quantum rotor states with a common dynamic exponent $z=2$. For the diluted lattice, the scaling works only for small $langle m^z_srangle$, indicating a mixture of different relaxation time scaling between the low energy states." @default.
• W2595498794 created "2017-03-23" @default.
• W2595498794 creator A5033845918 @default.
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• W2595498794 date "2017-08-28" @default.
• W2595498794 modified "2023-09-24" @default.
• W2595498794 title "Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets" @default.
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• W2595498794 doi "https://doi.org/10.1103/physrevb.96.054442" @default.
• W2595498794 hasPublicationYear "2017" @default.
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