Research: Continuous matrix product operator approach for finite temperature quantum states

Strong correlations between the constituent particles often lead to novel quantum phenomena, such as the fractional quantum Hall effect and the high-temperature superconductivity. Reliable numerical methods play an essential role in studying these strongly correlated systems. Among them, tensor network methods, such as the density matrix renormalization group, have been very successful in studying ground-state properties at zero temperature. At finite temperature, tensor network methods are, however, less satisfactory and are under continuous development.

Along this direction, we have made an important progress by designing a new tensor-network algorithm based on the continuous matrix product operator. Our method works in the thermodynamic limit and handles short-range and long-range interactions on equal footing, without discretizing the imaginary time. Moreover, it provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions, which are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation. This opens up an exciting possibility for the synergy between computations and experiments.

W. Tang, H.-H. Tu, L. Wang,
Continuous Matrix Product Operator Approach to Finite Temperature Quantum States,
Phys. Rev. Lett. 125, 170604 (2020) (arXiv)