Real-time dynamics in spin-1/2 chains with adaptive time-dependent density matrix renormalization group.

Area of Science:

• Condensed Matter Physics
• Quantum Magnetism
• Many-Body Systems

Background:

• Antiferromagnetic spin 1/2 XXZ chains exhibit complex magnetic properties.
• Understanding magnetization transport is crucial for quantum information and materials science.

Purpose of the Study:

• To investigate the impact of interaction strengths and dimerization on magnetization transport.
• To analyze the accuracy of adaptive time-dependent density-matrix renormalization group (t-DMRG) for these systems.

Main Methods:

• Utilized adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG).
• Simulated real-time evolution of an inhomogeneous initial state.
• Analyzed error sources in adaptive t-DMRG by comparing with the exactly solvable XX model.

Main Results:

• Ballistic magnetization transport observed for weak S(z)S(z) interactions and any dimerization.
• Magnetization transport is significantly suppressed for stronger S(z)S(z) interactions, with a sharp crossover at J(z)=1.
• Identified Trotter decomposition as the dominant error source at short times and DMRG truncation error at longer times, with a crossover to a
• runaway
• time.

Conclusions:

• The S(z)S(z) interaction strength critically determines magnetization transport in these systems.
• Adaptive t-DMRG provides accurate results for magnetization transport within accessible time scales.
• Error analysis reveals distinct regimes dominated by different numerical approximations in adaptive t-DMRG.