Locally accurate matrix product approximation to thermal states

• URL: http://arxiv.org/abs/2106.03854v2
• Date: Wed, 25 Aug 2021 23:33:40 GMT
• Title: Locally accurate matrix product approximation to thermal states
• Abstract summary: We prove that a thermal state at constant inverse temperature $beta$ has a matrix product representation with bond dimension $etilde O(sqrtbetalog (1/epsilon))$ 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.
• Score: 2.741266294612776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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