Rigorous RG algorithms and area laws for low energy eigenstates in 1D
Thomas Vidick, California Institute of Technology
One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. We give a new algorithm for finding low energy states for 1D systems, based on a rigorously justified RG type transformation. Our algorithm works in settings were an area law was not even known to hold (but we prove one as a by-product of our approach), including a polynomial time algorithm for n-qudit local Hamiltonians with poly(n)-degenerate ground spaces and a quasi-polynomial time algorithm for the poly(n) lowest energy states for 1D systems without energy gap (but under a mild density condition). I will also describe recent numerical results comparing our algorithm with DMRG on some degenerate or critical models of interest.
Based on joint work with Itai Arad, Zeph Landau and Umesh Vazirani (arXiv:1602.08828) and Brenden Roberts and Olexei I. Motrunich (arXiv:1703.01994).
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