Abstract
The extensivity of the quantum Hirota model’s conservation laws on a 1 + 1 dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a continuous family of quasilocal conservation laws from the conserved operators proposed by Faddeev and Volkov. The Hilbert–Schmidt kernel which allows the calculation of inner products of these new conservation laws is explicitly computed. This result has potential applications in quantum quench and transport problems in integrable quantum field theories.
Highlights
In recent years, the study of integrable systems out of equilibrium has become one of the main focuses of theoretical and mathematical physics [1]
Understanding the local and quasilocal‡ conservation laws and their impact on the non-equilibrium dynamics of integrable systems has become an important problem of quantum statistical physics
We note that an alternative procedure to construct quasilocal charges in the integrable field theories with non-diagonal scattering, which builds on the discrete light cone approach with fermionic variables of Destri and De Vega [7, 14, 15], has been suggested in Ref. [13]
Summary
The study of integrable systems out of equilibrium has become one of the main focuses of theoretical and mathematical physics [1]. Conservation laws varying linearly in the system size, as measured by the Hilbert-Schmidt norm, can be used in the Mazur-Suzuki bound to rigorously establish the ballistic transport at high temperatures [3] Until now these ideas have been implemented mainly in the paradigmatic example of integrable systems, the spin-1/2 XXZ model. The quasilocal conservation laws of the quantum Hirota model are identified for a generic rootof-unity quantization parameter, where the local Hilbert space is finite dimensional. The last two sections, 4 and 5, constitute the explanation of the results – in Section 4 linear extensivity of charges (4) is established, following the procedure proposed in [10], while in Section 5 the Hilbert-Schmidt kernel is explicitly computed and an explicit matrix product form of the conserved charges is spelled out. § Note that this inner product is semi-definite since, in addition to 0, all operators of the form α1 with α ∈ C have HS norm equal to 0
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