Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm.

Area of Science:

• Quantum Many-Body Physics
• Quantum Field Theory
• Computational Physics

Background:

• Matrix product states (MPS) are generalized to continuous systems (cMPS) for studying 1D quantum field theories.
• Current cMPS ground state approximations rely on computationally expensive Euclidean time evolution simulations.

Purpose of the Study:

• To develop and demonstrate a novel cMPS optimization algorithm based on energy minimization using gradient methods.
• To achieve significant computational speed-ups compared to Euclidean time evolution for cMPS ground state calculations.

Main Methods:

• Proposed a cMPS optimization algorithm utilizing gradient-based energy minimization.
• Applied the algorithm to the Lieb-Liniger model in the thermodynamic limit.
• Compared computational performance against Euclidean time evolution methods.

Main Results:

• Achieved a computational speed-up exceeding two orders of magnitude compared to Euclidean time evolution.
• Enabled the simulation of much larger cMPS bond dimensions (e.g., D=256) with moderate resources.
• Demonstrated the algorithm's effectiveness for ground state studies in the thermodynamic limit.

Conclusions:

• The proposed gradient-based cMPS optimization offers a substantial computational advantage.
• This method unlocks the potential of cMPS for studying complex quantum systems.
• Facilitates more accurate and efficient ground state investigations in one-dimensional quantum field theories.