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Quantum Matter Seminar

Wednesday, December 1, 2021
4:00pm to 5:00pm
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East Bridge 201 (Richard P. Feynman Lecture Hall)
Pivot Hamiltonians: a tale of symmetry, entanglement, and quantum criticality
Nat Tantivasadakarn, Harvard,

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.

For more information, please contact Tracy Mikuriya by phone at (626)395-8579 or by email at [email protected].