Dynamics of one-dimensional spin models via complex-time evolution of tensor networks

Area of Science:

• Quantum physics
• Condensed matter theory
• Computational physics

Background:

• Studying real-time dynamics of strongly correlated quantum systems is challenging.
• Density Matrix Renormalization Group (DMRG) and tensor network methods have advanced this field.
• Complex-time evolution was introduced to manage entanglement in tensor network states.

Purpose of the Study:

• Investigate the dynamics of one-dimensional spin systems using complex-time evolution.
• Analyze the transverse-field Ising model (TFIM) and the XXZ model.
• Assess the efficacy of complex-time evolution in managing entanglement growth.

Main Methods:

• Employed a complex-time evolution scheme for tensor network states.
• Applied the method to one-dimensional spin systems: TFIM and XXZ model.
• Performed analysis of dynamic critical exponent and dynamical structure factor.

Main Results:

• Complex-time evolution successfully reproduced real-time evolution results.
• The method significantly mitigated the rapid growth of quantum entanglement.
• Successfully revisited the dynamic critical exponent z of the TFIM.
• Explored the dynamical structure factor in gapped and gapless states of the XXZ model.

Conclusions:

• Complex-time evolution combined with extrapolation is a robust framework for quantum dynamics.
• This approach enables efficient and comprehensive study of complex quantum systems.
• Offers a powerful tool for understanding the behavior of strongly correlated systems.