Continuous Matrix Product Operator Approach to Finite Temperature Quantum States

Area of Science:

• Quantum physics
• Condensed matter theory

Background:

• Studying quantum systems at finite temperatures is crucial for understanding many physical phenomena.
• Existing methods often face challenges with long-range interactions or time discretization errors.

Purpose of the Study:

• To present a novel algorithm for simulating quantum systems at finite temperatures.
• To overcome limitations of existing numerical techniques for quantum many-body problems.

Main Methods:

• Utilizing a continuous matrix product operator (CMPO) representation.
• Handling both short-range and long-range interactions in the thermodynamic limit.
• Avoiding time discretization errors.

Main Results:

• The algorithm provides direct access to physical observables like specific heat and spectral functions.
• Successful verification on quantum XXZ chains.
• Application to quantum Ising models with power-law interactions and on an infinite cylinder.

Conclusions:

• The CMPO approach is a powerful tool for finite-temperature quantum system studies.
• The method offers accurate predictions relevant for quantum simulators and NMR relaxation rate experiments.