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.

26 pages, 3 figures; v2: minor revision and references added; v3: minor revision and appendix added

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• Quantum quenches in 1+1 dimensional conformal field theories
• Quasilocal charges in integrable lattice systems
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Exact solution for the quench dynamics of a nested integrable system
• Integrability-protected adiabatic reversibility in quantum spin chains
• Current operators in integrable spin chains: lessons from long range deformations
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Onsager symmetries in $U(1)$-invariant clock models
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Integrable quenches in nested spin chains I: the exact steady states
• Prethermalization at Low Temperature: the Scent of Long-Range Order
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Quantum quench in the attractive regime of the sine-Gordon model
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
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• Lack of thermalization for integrability-breaking impurities
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• Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
• Integrable Quantum Circuits from the Star-Triangle Relation
• Correlation and entanglement spreading in nested spin chains
• Popcorn Drude weights from quantum symmetry
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench