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Speaker: Eli Chertkov, University of Illinois, Urbana-Champaign
Title: Hunting for Hamiltonians: an inverse approach to quantum physics
Abstract: Traditionally, interacting quantum systems have been studied using a forward approach, where a Hamiltonian is solved to determine a system’s properties. In this talk, I will discuss an alternative inverse approach where we instead start with physical properties, such as eigenstates or symmetries, as input and look for Hamiltonians as output. I will describe two algorithms that we developed for solving this inverse problem, which can be implemented using a wide range of numerical methods. I will show how these algorithms can be used to find new Hamiltonians with interesting physics, such as Hamiltonians with frustrated ground states, quantum spin liquid Hamiltonians, and Hamiltonians with exotic Majorana zero modes. Time permitting, I will also briefly explain recent applications and extensions of these methods in areas such as many-body localization and the reconstruction of Hamiltonians from thermal states.