Locally accurate matrix product approximation to thermal states

Abstract

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.

arXiv commentv2: abstract and introduction expanded

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Cited by in corpus (2)

• Quantum many-body systems in thermal equilibrium
• Learning quantum many-body systems from a few copies