A polynomial-time algorithm for the ground state of one-dimensional gapped Hamiltonians

Abstract

A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\hat{I}\mu ,n,\hat{I}\cdot$ be the energy gap, the system size, and the desired precision, respectively. Neglecting $\hat{I}\mu$-dependent subpolynomial (in $n$) and constant factors, the running time of the algorithm is $n^{O(1)}$ for $\hat{I}\cdot =n^{-O(1)}$.