Extracting the Speed of Light from Matrix Product States

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Computational Physics

Background:

• Matrix product state (MPS) simulations are powerful tools for studying one-dimensional quantum systems.
• Understanding the dynamics and critical properties of these systems often involves determining characteristic velocities.

Purpose of the Study:

• To establish a precise method for calculating the speed of light in quantum systems using MPS simulations.
• To apply this method to determine critical velocities in challenging systems like non-integrable Heisenberg chains and doped Hubbard ladders.

Main Methods:

• Comparing the spectra of the local effective Hamiltonian and the transfer operator in infinite-system MPS simulations.
• Utilizing a path integral perspective to derive the correspondence between these spectral properties.
• Applying the developed technique to SU(2) Heisenberg chains and doped Hubbard ladders.

Main Results:

• Demonstrated the identity between the local effective Hamiltonian and transfer operator spectra, up to a rescaling factor (the system's speed of light).
• Achieved highly accurate estimations of the speed of light for critical SU(2) Heisenberg chains with S>1/2.
• Obtained precise velocities for doped Hubbard ladders across various doping levels.
• Calculated the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders with improved accuracy.

Conclusions:

• The spectral comparison method provides a highly accurate and practical way to determine the speed of light in quantum systems.
• This technique overcomes limitations of previous methods for analyzing critical phenomena in complex quantum models.
• The findings offer new insights into the properties of strongly correlated electron systems.