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

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.

Spin chain overlaps and the twisted Yangian

“…which is a constant solution to the BYB. Overlaps and quantum quenches for this state were considered in [6,7] where it was found that the overlap is of the form ( are indeed free of singularities within the physical strip. Going further, we can compute the higher Y -functions from the Y -system (3.23).…”

One-point functions in AdS/dCFT

“…Finally, there are a lot of interesting directions in related fields as well. We already mentioned the close link to quantum quenches and our understanding of integrability in nested systems is still incomplete and under development [31,32]. A different interesting avenue is that of the boundary bootstrap program [58].…”

“…In [29,[31][32][33][34] it was shown for wide range of spin chains that integrable initial states factorize into a product of two site states |ψ 0 ∼ K ab |ab . The matrix K ab is related to an integrable reflection matrix.…”

Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

“…This quench was studied in [37,38] where the exact root densities were determined using Boundary Quantum Transfer Matrix methods. Now we computed the mean values of the first two members X 1 (u) and Y 1 (u) in this initial state and we checked that the relations (6.18) indeed hold.…”

“…In the following we compute the mean values of the charges X 1 (u) and Y 1 (u) in |Ψ δ using their definition: From this we will compute the hole densities directly from the string-charge relations (6.15), which will be compared to (C.5). The above mean values can be evaluated using standard methods, by building the corresponding 2D partition functions, and evaluating them with double row transfer matrices in the crossed channel [21,37,38], see also Fig. 5.…”