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

TL;DR

This paper investigates the short-imaginary-time quantum critical dynamics in the J-Q3 spin chain, revealing a marginal initial order parameter and distinct relaxation behavior compared to Ising transitions.

Contribution

It introduces a scaling analysis of SITQCD in the J-Q3 chain, identifying a marginal operator and characterizing the critical point and exponents.

Findings

Critical point at q_c=0.170(14)

Initial slip exponent θ=-0.507(3)

Scaling dimension of initial order parameter close to zero

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 $q_{\rm c}=0.170(14)$. 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.