Popcorn Drude weights from quantum symmetry

Abstract

Integrable models provide emblematic examples of non-ergodic phenomena. One of their most distinguished properties are divergent zero-frequency conductivities signalled by finite Drude weights. Singular conductivities owe to long-lived quasiparticle excitations that propagate ballistically through the system without any diffraction. The case of the celebrated quantum Heisenberg chain, one of the best-studied many-body paradigms, turns out to be particularly mysterious. About a decade ago, it was found that the spin Drude weight in the critical phase of the model assumes an extraordinary, nowhere continuous, dependence on the anisotropy parameter in the shape of a `popcorn function'. This unprecedented discovery has been afterwards resolved at the level of the underlying deformed quantum symmetry algebra which helps explaining the erratic nature of the quasiparticle spectrum at commensurate values of interaction anisotropy. This work is devoted to the captivating phenomenon of discontinuous Drude weights, with the aim to give a broader perspective on the topic by revisiting and reconciling various perspectives from the previous studies. Moreover, it is argued that such an anomalous non-ergodic feature is not exclusive to the integrable spin chain but can be instead expected in a number of other integrable systems that arise from realizations of the quantum group ${\mathcal{U}}_q(\mathfrak{sl}(2))$, specialized to unimodular values of the quantum deformation parameter $q$. Our discussion is framed in the context of gapless anisotropic quantum chains of higher spin and the sine-Gordon quantum field theory in two space-time dimensions.

arXiv comment58 pages. To appear in Focus Collection on "Hydrodynamics of Low-Dimensional Quantum Systems''

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• Thermodynamics and fractal Drude weights in the sine-Gordon model
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Dynamical separation of charge and energy transport in one-dimensional Mott insulators
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Anomalous charge transport in the sine-Gordon model