We investigate the short-time quantum critical dynamics in the imaginary-time relaxation processes of finite-size systems. Universal scaling behaviors exist in the imaginary-time evolution. In particular, the system undergoes a critical initial slip stage characterized by an exponent $\ensuremath{\theta}$, in which an initial power-law increase emerges in the imaginary-time correlation function when the initial state has a zero order parameter and a vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo (QMC) simulations. In the one-dimensional case, we locate the quantum critical point at ${(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)$ in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length $L=32--256$ and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by $3.044\phantom{\rule{0.16em}{0ex}}51(7)$ in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size $L=24$ --64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.We investigate the short-time quantum critical dynamics in the imaginary-time relaxation processes of finite-size systems. Universal scaling behaviors exist in the imaginary-time evolution. In particular, the system undergoes a critical initial slip stage characterized by an exponent $\ensuremath{\theta}$, in which an initial power-law increase emerges in the imaginary-time correlation function when the initial state has a zero order parameter and a vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo (QMC) simulations. In the one-dimensional case, we locate the quantum critical point at ${(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)$ in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length $L=32--256$ and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by $3.044\phantom{\rule{0.16em}{0ex}}51(7)$ in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size $L=24$--64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.

arXiv:1705.05931Physical review. B./Physical review. BSep 12, 201717 citations

Universality and scaling in short-time critical dynamics

Keisuke Okano, Lothar Schülke, K. Yamagishi +1 more

arXiv:cond-mat/9601037Nuclear Physics BFeb 1, 199783 citations

Critical slowing down in local dynamics simulations

Hans-O Heuer

The author reports some universal and non-universal aspects of the critical dynamics of the three-dimensional Ising model, obtained in extensive Monte Carlo finite-size simulations. The author shows that the time-dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point: (i) phase fluctuations from one metastable minimum of the free energy to the other, dominating the long-time behaviour of the magnetization; (ii) critical fluctuations inside each minimum, decaying on a comparatively short timescale. Both kinds of fluctuations show up the same critical exponent z=2.10+or-0.02, which is also in excellent agreement with the exponent z of energy fluctuations.The author reports some universal and non-universal aspects of the critical dynamics of the three-dimensional Ising model, obtained in extensive Monte Carlo finite-size simulations. The author shows that the time-dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point: (i) phase fluctuations from one metastable minimum of the free energy to the other, dominating the long-time behaviour of the magnetization; (ii) critical fluctuations inside each minimum, decaying on a comparatively short timescale. Both kinds of fluctuations show up the same critical exponent z=2.10+or-0.02, which is also in excellent agreement with the exponent z of energy fluctuations.

Journal of Physics A Mathematical and GeneralMay 7, 199225 citations

Universality in Critical Dynamics: a Quantum Monte Carlo Study

Peter Nightingale

APSMar 1, 19980 citations

{(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)

in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length

L=32--256

and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by

3.044\phantom{\rule{0.16em}{0ex}}51(7)

in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size

L=24

--64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.