Quantum Physics

    

Locally Accurate Matrix Product Approximation to Thermal States

Authors: Yichen Huang

In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We prove that a thermal state at constant inverse temperature $\beta$ has a matrix product representation with bond dimension $e^{\tilde O(\sqrt{\beta\log(1/\epsilon)})}$ such that all local properties are approximated to accuracy $\epsilon$. This justifies the common practice of using a constant bond dimension in the numerical simulation of thermal properties.

Comments: 5 Pages. v2: abstract and introduction expanded. Science Bulletin 66 (24), 2456, 2021. https://doi.org/10.1016/j.scib.2021.08.011 open access link: https://engine.scichina.com/doi/pdf/B282729F14C64621A4B6C7C16E05C372

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Submission history

[v1] 2021-06-07 13:58:46
[v2] 2021-09-16 15:02:23

Unique-IP document downloads: 279 times

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