Quasi-local conserved charges and spin transport in spin-1 integrable chains

Abstract

We consider the integrable one-dimensional spin-1 chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-1/2 model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-1 Babujian-Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-1 ZF chain. Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded. Using the Mazur inequality, we show that, as for the XXZ model, these quasi-local charges are enough to prove that the high-temperature spin Drude weight is non-vanishing in the thermodynamic limit, thus establishing ballistic spin transport at high temperature.

Current operators in integrable spin chains: lessons from long range deformations

“…Typically the amplitudes decay exponentially with the range. The quasi-local operators play an essential role in the description of the Generalized Gibbs Ensemble of Heisenberg spin chain and related models [17,18,19,20,21,22]. There a commuting set of quasi-local charges is derived from the fused transfer matrices.…”

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

“…Amazingly, many of these examples have been experimentally realized [9][10][11][12][13][14][15][16][17].Integrable models are characterized by the presence of infinitely many conserved chargesQ j , which can be used to exactly determine their thermodynamics [25]. In recent times, the importance of quasi-local charges has moreover been underlined [26][27][28][29][30][31][32][33][34][35].The last decade has witnessed exact results reaching out-of-equilibrium protocols as well: great attention has been devoted to the homogeneous sudden quantum quench [36] (see also Ref. [37] and reference therein).…”

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

“…Our charges and the currents associated with them can also be used to generalize the recently proposed integrable hydrodynamics description of transport phenomena [105] for non-diagonal scattering theories. Finally, the construction of additional charges in sine-Gordon following our procedure seems to be adaptable to the further set of "non-unitary" charges, which in the XXZ case have found applications in the study of spin transport [64,65,70,71]. It would be interesting to understand the meaning of these charges in the sine-Gordon model, as well as possible applications to its transport properties [106].…”

“…As was first unveiled recently in the context of the XXZ chain in a series of papers by Prosen and collaborators (see in particular [64][65][66][67][68]72] as well as [69] for a review, and [70] by different authors and [71,74] for generalizations to chains of higher spin), the algebraic structures underlying quantum integrable lattice models may allow for more conserved charges to be built, which have a weaker (but still physically essential) form of locality called quasilocality. This term indicates that such charges can be written as sums of densities with arbitrarily large support, but with Hilbert-Schmidt norm decreasing exponentially with the length of the support.…”