We revisit the numerical problem of computing the high temperature spin stiffness, or Drude weight, D of the spin-1/2 XXZ chain using exact diagonalization to systematically analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero total magnetization, we find D vanishes exactly due to spin-inversion symmetry for all but the anisotropies∆MN = cos(πM/N ) with N, M ∈ Z + coprimes and N > M , provided system sizes L ≥ 2N , for which states with different spin-inversion signature become degenerate due to the underlying sl2 loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on data from the system sizes and anisotropies∆MN (with N < L/2) available to us] to dominate the grand-canonical ensemble evaluation of D in the thermodynamic limit. Including a magnetic flux not only breaks spin-inversion in the zero magnetization sector but also lifts the loop-algebra degeneracies in all symmetry sectors -this effect is more pertinent at smaller ∆ due to the larger contributions to D coming from the low-magnetization sectors which are more sensitive to the system's symmetries. Thus we generically find a finite D for fluxed rings and arbitrary 0 < ∆ < 1 in both ensembles. In contrast, at the isotropic point and in the gapped phase (∆ ≥ 1) D is found to vanish in the thermodynamic limit, independent of symmetry or ensemble. Our analysis demonstrates how convergence to the thermodynamic limit within the gapless phase (∆ < 1) may be accelerated and the finite-size anomalies overcome: D extrapolates nicely in the thermodynamic limit to either the recently computed lower-bound or the Thermodynamic Bethe Ansatz result provided both spin-inversion is broken and the additional degeneracies at the∆MN anisotropies are lifted.

We study magnetization transport in anisotropic spin-1/2 chains governed by the integrable XXZ model with and without integrability-breaking perturbations at high temperatures (T → ∞) using a hybrid approach that combines exact sum-rules with judiciously chosen Ansätze. In the integrable XXZ model we find (i) super-diffusion at the isotropic (Heisenberg) point, with frequency dependent conductivity σ ′ (ω → 0) ∼ |ω| α , where α = −3/7 in close numerical agreement with recent t-DMRG computations; (ii) a continuously drifting exponent from α = −1 + in the XY limit of the model to α > 0 within the Ising regime; and (iii) a diffusion constant saturating in the XY coupling deep in the Ising limit. We consider two kinds of integrability breaking perturbations -a simple next-nearestneighbor spin-flip term (J2) and a three-spin assisted variant (t2), natural in the fermion particle representation of the spin chain. In the first case we discover a remarkable sensitivity of σ ′ (ω) to the sign of J2, with enhanced low frequency spectral weight and a pronounced upward shift in the magnitude of α for J2 > 0. Perhaps even more surprising, we find sub-diffusion (α > 0) over a range of J2 < 0. By contrast, the effects of the "fermionic" three-spin perturbation are sign symmetric; this perturbation produces a clearly observable hydrodynamic relaxation. At large strength of the integrability breaking term J2 → ±∞ the problem is effectively non-interacting (fermions hopping on odd and even sublattices) and we find α → −1 behavior reminiscent of the XY limit of the XXZ chain. Exact diagonalization studies largely corroborate these findings at mid-frequencies.

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Deep neural network models represent the stateof-the-art methodologies for natural language processing. Here we build on top of these methodologies to incorporate temporal information and model how review data changes with time. Specifically, we use the dynamic representations of recurrent point process models, which encode the history of how business or service reviews are received in time, to generate instantaneous language models with improved prediction capabilities. Simultaneously, our methodologies enhance the predictive power of our point process models by incorporating summarized review content representations. We provide recurrent network and temporal convolution solutions for modeling the review content. We deploy our methodologies in the context of recommender systems, effectively characterizing the change in preference and taste of users as time evolves. Source code is available at [1]. Index Terms-dynamic language models, marked point processes, recommender systems We present the related work in Section II and introduce our model in Section III. The baseline models used for comparison in this paper are presented in Section IV. The experimental setup and results are presented in Section V. Finally, in Section VI we conclude and discuss future work.