PIRSA:21110042

Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality

Tantivasadakarn, N. (2021). Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality. Perimeter Institute. https://pirsa.org/21110042

Tantivasadakarn, Nathanan. Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality. Perimeter Institute, Nov. 29, 2021, https://pirsa.org/21110042 

          @misc{ pirsa_PIRSA:21110042,
            doi = {10.48660/21110042},
            url = {https://pirsa.org/21110042},
            author = {Tantivasadakarn, Nathanan},
            keywords = {Condensed Matter},
            language = {en},
            title = {Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {nov},
            note = {PIRSA:21110042 see, \url{https://pirsa.org}}
          }

Nathanan Tantivasadakarn California Institute of Technology (Caltech)

DOI 10.48660/21110042
Collection
Talk Type Scientific Series
Subject

Abstract

I will introduce the notion of Pivot Hamiltonians, a special class of Hamiltonians that can be used to "generate" both entanglement and symmetry. On the entanglement side, pivot Hamiltonians can be used to generate unitary operators that prepare symmetry-protected topological (SPT) phases by "rotating" the trivial phase into the SPT phase. This process can be iterated: the SPT can itself be used as a pivot to generate more SPTs, giving a rich web of dualities. Furthermore, a full rotation can have a trivial action in the bulk, but pump lower dimensional SPTs to the boundary, allowing the practical application of scalably preparing cluster states as SPT phases for measurement-based quantum computation. On the symmetry side, pivot Hamiltonians can naturally generate U(1) symmetries at the transition between the aforementioned trivial and SPT phases. The sign-problem free nature of the construction gives a systematic approach to realize quantum critical points between SPT phases in higher dimensions that can be numerically studied. As an example, I will discuss a quantum Monte Carlo study of a 2D lattice model where we find evidence of a direct transition consistent with a deconfined quantum critical point with emergent SO(5) symmetry.

This talk is based on arXiv:2107.04019, 2110.07599, 2110.09512