A multi-layer multi-configurational time-dependent Hartree approach to lattice models beyond one dimension

Area of Science:

• Quantum Dynamics
• Condensed Matter Physics
• Computational Quantum Chemistry

Background:

• The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is a powerful tool for quantum dynamics.
• Studying quantum fluids, especially in multi-dimensional lattice models at finite temperatures, presents significant computational challenges.

Purpose of the Study:

• To explore the applicability of the multi-layer MCTDH approach for describing quantum fluids.
• To adapt and apply the multi-layer MCTDH method to multi-dimensional lattice models beyond one dimension.
• To investigate the simulation of finite temperature phase transitions in quantum systems.

Main Methods:

• Utilized the multi-layer MCTDH approach in its second quantization representation.
• Developed a scheme to map multi-dimensional lattice sites onto the MCTDH tree representation.
• Adapted a statistical sampling scheme for efficient thermal ensemble description.
• Applied the method to a two-dimensional hard-core Bose-Hubbard model up to 64x64 lattice sites.

Main Results:

• Demonstrated that the required basis set size for convergence does not scale with lattice size.
• Successfully simulated the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.
• The proposed mapping and sampling schemes proved effective for multi-dimensional systems.

Conclusions:

• The multi-layer MCTDH approach is a scalable and efficient method for studying quantum fluids in multi-dimensional lattice models.
• The method provides accurate simulations of quantum phenomena, including critical phase transitions at finite temperatures.
• This work extends the capabilities of MCTDH for complex condensed matter systems.