Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain

Abstract

We study the short-imaginary-time quantum critical dynamics (SITQCD) in the J-Q${}_3$ spin chain, which hosts a quasi-long-range-order phase to a valence bond solid transition. By using the scaling form of the SITQCD with a saturated ordered phase, we are able to locate the critical point at $q_{\mathrm{c}}=0.170(14)$. We also obtain the critical initial slip exponent $\theta =-0.507(3)$ and the static exponent $\beta /\nu =0.498(2)$. More strikingly, we find that the scaling dimension of the initial order parameter $x_0$ is close to zero, which suggests that the initial order parameter is a marginal operator. As a result, there is no initial increase behavior of the order parameter in the short-imaginary-time relaxation process for this model, which is very different from the relaxation dynamics in the Ising-type phase transitions. Our numerical results are realized by the projector quantum Monte Carlo algorithm.

arXiv comment8 pages, 8 figures

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