Interacting Topological Matter: Atomic, Molecular and Optical Systems05 June 2021
On Monday June 7th I'll be presenting various results on Floquet-engineering counterdiabatic protocols at the KITP program on Interacting Topological Matter: Atomic, Molecular and Optical Systems. I'll be in good company — check out the full program, focusing on Floquet systems, here. A recording of the talk will also appear online afterwards.
Correlations and commuting transfer matrices in integrable unitary circuits02 June 2021
Our paper on Correlations and commuting transfer matrices in integrable unitary circuits just appeared on the arXiv! We continue our study of unitary circuits, this time focusing on the calculation of correlations functions in circuits constructed out of R-matrices from integrability. We construct a transfer matrix approach, and show how the integrability leads to a family of commmuting transfer matrices with a rich underlying structure. Joint work with Austen Lamacraft and Jonah Herzog-Arbeitman.
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.