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Thermodynamic limit of Mazur bound on the spin stiffness of XXZ chain, using the almost-conserved Z-operator

Tomaž Prosen

This short note can be considered as a mathematical supplement to [Phys. Rev. Lett. 106, 217206 (2011)], namely explaining in more detail how rigorous bound on high-temperature spin stiffness is established in thermodynamic limit using the almost-conserved Z-operator resulting from solving the boundary driven Lindblad equation for the anisotropic Heisenberg (XXZ) spin 1/2 chain . No reference to techniques used in Suzuki's proofs of Mazur's bound is made, but quasi-local spin C* algebras and Lieb-Robinson bounds are invoked instead.This short note can be considered as a mathematical supplement to [Phys. Rev. Lett. 106, 217206 (2011)], namely explaining in more detail how rigorous bound on high-temperature spin stiffness is established in thermodynamic limit using the almost-conserved Z-operator resulting from solving the boundary driven Lindblad equation for the anisotropic Heisenberg (XXZ) spin 1/2 chain . No reference to techniques used in Suzuki's proofs of Mazur's bound is made, but quasi-local spin C* algebras and Lieb-Robinson bounds are invoked instead.

arXiv:1109.3124Sep 14, 20110 citations

A remark on the Kochen-Specker Theorem

Andrew Lenard

Springer eBooksJan 1, 19744 citations

Metrological detection of multipartite entanglement through dynamical symmetries

Yu-Ran Zhang, Franco Nori

Multipartite entanglement, characterized by the quantum Fisher information (QFI), plays a central role in quantum-enhanced metrology and understanding quantum many-body physics. With a dynamical generalization of the Mazur-Suzuki relations, we provide a rigorous lower bound on the QFI for the thermal Gibbs states in terms of dynamical symmetries, i.e., operators with periodic time dependence. We demonstrate that this bound can be saturated when considering a complete set of dynamical symmetries. Moreover, this lower bound with dynamical symmetries can be generalized to the QFI matrix and to the QFI for the thermal pure states, predicted by the eigenstate thermalization hypothesis. Our results reveal a new perspective to detect multipartite entanglement and other generalized variances in an equilibrium system, from its nonstationary dynamical properties, and is promising for studying emergent nonequilibrium many-body physics.Multipartite entanglement, characterized by the quantum Fisher information (QFI), plays a central role in quantum-enhanced metrology and understanding quantum many-body physics. With a dynamical generalization of the Mazur-Suzuki relations, we provide a rigorous lower bound on the QFI for the thermal Gibbs states in terms of dynamical symmetries, i.e., operators with periodic time dependence. We demonstrate that this bound can be saturated when considering a complete set of dynamical symmetries. Moreover, this lower bound with dynamical symmetries can be generalized to the QFI matrix and to the QFI for the thermal pure states, predicted by the eigenstate thermalization hypothesis. Our results reveal a new perspective to detect multipartite entanglement and other generalized variances in an equilibrium system, from its nonstationary dynamical properties, and is promising for studying emergent nonequilibrium many-body physics.

arXiv:2304.00564Apr 2, 20230 citations

A Remark concerning the Bogoliubov Theory

John M. Blatt

Progress of Theoretical PhysicsMar 1, 19590 citations

On a conjecture of C.N. Yang

James S. Bell

Physics LettersSep 1, 19626 citations

Exact Mazur bounds in the pair-flip model and beyond

Oliver Hart

By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general p-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as 1/ \sqrt{L} L , rather than 1/L, as had previously been thought. This result implies that the nontrivial conserved operators implied by p-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general p-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as 1/ \sqrt{L} L , rather than 1/L, as had previously been thought. This result implies that the nontrivial conserved operators implied by p-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.

arXiv:2308.00738SciPost Physics CoreJul 4, 20244 citations

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