Thursday Nov 7 1pm AEDT 

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Abstract:  Frustration-free quantum models represent a class of models where the Hamiltonian is a sum of local projectors, and the ground state minimizes the energy of all these local projectors simultaneously. However, "to know whether a given Hamiltonian is frustration-free or not" is a question that is widely believed to be intractable, as it belongs to a k-QSAT (quantum satisfaction problem) known to be QMA_1-complete -- a quantum analogue of the NP-complete class for classical problems. Beyond a simple "yes or no," condensed matter physics also seeks to understand the nature of ground states that may arise from these models. In this work, we introduce an algorithm that not only determines frustration-free ground states but also constructs them as "cluster-projected matrix product states" (MPS). Our method progressively builds the MPS by starting with a single-site tensor and incrementally adding tensors for each site. Each tensor element is chosen by applying projectors that impose local constraints, ensuring the wave function aligns with the desired configuration of local basis states. This algorithm is applicable to models such as the Motzkin and Fredkin chains, zigzag frustrated magnets, and lattices like diamond, triangular, kagome, and square structures. Our approach captures gapless and long-range entangled ground states for systems up to a hundred sites, depending on the model, and works for both one- and two-dimensional systems. Notably, it can even describe the long-range entangled spin liquid state in the two-dimensional toric code model, distinguishing all the topological sectors very easily.
[1]  H. Saito and C.Hotta,  Phys. Rev. Lett, 132 , 166701 (2024)
[2]  H. Saito and C. Hotta, arXiv:2406.12357.