Universal short-time quantum critical dynamics of finite-size systems

Article

关键词: SPONTANEOUS SYMMETRY-BREAKING;    MATRIX RENORMALIZATION-GROUP;    MONTE-CARLO;    ISING-MODEL;    CRITICAL EXPONENTS;    CRITICAL RELAXATION;    PHASE-TRANSITIONS;    TRANSVERSE FIELD;    SPIN SYSTEMS;    BOSE-GAS;   

DOI  :  10.1103/PhysRevB.96.094304

来源: SCIE

【 摘 要 】

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., 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 03(8) in the thermodynamic limit, and we estimate the critical initial slip exponent theta = 0.3734(2) and the static exponent beta/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 51(7) in the thermodynamic limit, while the critical exponents are theta = 0.209(4) and beta/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.

【 授权许可】

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