Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model

Area of Science:

• Quantum Mechanics
• Computational Physics

Background:

• Open quantum systems describe interactions between quantum systems and their environment.
• Accurate numerical simulations are crucial for understanding complex quantum phenomena.

Purpose of the Study:

• To present a general numerical approach for simulating open quantum systems.
• To enable efficient and accurate calculations of static, spectral, and dynamic properties.
• To demonstrate the method's efficacy using the spin-boson model.

Main Methods:

• Combines polynomial expansions of spectral functions with sparse grid interpolation.
• Constructs a moderate-dimension Hilbert space for bath degrees of freedom.
• Utilizes standard exact diagonalization algorithms.

Main Results:

• Achieves highly accurate and efficient calculations for open quantum systems.
• Successfully simulates phase transitions, critical behavior, and dissipative spin dynamics.
• Demonstrates the method's applicability to the spin-boson model.

Conclusions:

• The proposed numerical approach offers a powerful tool for studying open quantum systems.
• The method provides accurate insights into quantum dynamics and critical phenomena.
• This technique enhances the simulation capabilities in quantum physics and condensed matter.