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arXiv · 1812.05330

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Lorenzo Piroli·Eric Vernier·Pasquale Calabrese·Balázs Pozsgay
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Abstract

We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to "soliton-non-preserving" boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain "fused operators" that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the $T$- and $Y$-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of $SU(3)$-invariant Hamiltonians with open boundary conditions.

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Lorenzo Piroli, Eric Vernier, Pasquale Calabrese, Balázs Pozsgay. 2019-05-13. Integrable quenches in nested spin chains II: fusion of boundary transfer matrices. https://doi.org/10.1088/1742-5468%2Fab1c52

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