Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating […]

A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the Marshall-Lieb-Mattis theorem, the Lieb theorem, and the stability theorem of Lieb ferrimagnetism. Next, I will outline a mathematical framework within which these theorems can be […]

We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed […]

Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating […]

A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the Marshall-Lieb-Mattis theorem, the Lieb theorem, and the stability theorem of Lieb ferrimagnetism. Next, I will outline a mathematical framework within which these theorems can be […]

We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed […]