Locally accurate matrix product approximation to thermal states.

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 β has a matrix product representation with bond dimension e √ β log(1/ )) such that all local properties are approximated to accuracy . This justifies the common practice of using a constant bond dimension in the numerical simulation of thermal properties.

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