Topological quantum phase transitions in exact two-dimensional isometric tensor networks - VIRTUAL

APA

Liu, Y. (2023). Topological quantum phase transitions in exact two-dimensional isometric tensor networks - VIRTUAL. Perimeter Institute for Theoretical Physics. https://pirsa.org/23120036

MLA

Liu, Yu-Jie. Topological quantum phase transitions in exact two-dimensional isometric tensor networks - VIRTUAL. Perimeter Institute for Theoretical Physics, Dec. 08, 2023, https://pirsa.org/23120036

BibTex

          @misc{ scivideos_PIRSA:23120036,
            doi = {10.48660/23120036},
            url = {https://pirsa.org/23120036},
            author = {Liu, Yu-Jie},
            keywords = {Other Physics},
            language = {en},
            title = {Topological quantum phase transitions in exact two-dimensional isometric tensor networks - VIRTUAL},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2023},
            month = {dec},
            note = {PIRSA:23120036 see, \url{https://scivideos.org/pirsa/23120036}}
          }
          

Yu-Jie Liu Technical University of Munich (TUM)

Source RepositoryPIRSA
Talk Type Scientific Series
Subject

Abstract

Isometric tensor networks (isoTNS) form a subclass of tensor network states that have an additional isometric condition, which implies that they can be efficiently prepared with a linear-depth quantum circuit. In this work, we introduce a procedure to construct isoTNS encoding of certain 2D classical partition functions. By continuously tuning a parameter in the isoTNS, the many-body ground state undergoes quantum phase transitions, exhibiting distinct 2D topological order. We illustrate this by constructing an isoTNS path with bond dimension $D = 2$ interpolating between distinct symmetry-enriched topological (SET) phases. At the transition point, the isoTNS wavefunction is related to a gapless point in the classical six-vertex model. Furthermore, the critical wavefunction supports a power-law correlation along one spatial direction while remains long-range ordered in the other spatial direction. We provide an exact linear-depth parametrized local quantum circuit that realizes the path. The above features can therefore be efficiently realized on a programmable quantum device. In the second part of my talk, I will show how to discover efficiently measurable order parameters for quantum phases using model-independent training of quantum circuit classifiers. The possibility of the efficient realization of phase transition path is useful for benchmarking quantum phase recognition methods in higher than one dimension.

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