Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

Abstract

We illustrate how finite-temperature charge and thermal Drude weights of one-dimensional systems can be obtained from the relaxation of initial states featuring global (left-right) gradients in the chemical potential or temperature. The approach is tested for spinless interacting fermions as well as for the Fermi-Hubbard model, and the behaviour in the vicinity of singular points (such as half filling or isotropic chains) is discussed. We present technical details on how to implement the calculation in practice using the density matrix renormalization group and show that the non-equilibrium dynamics is often less demanding to simulate numerically and features simpler finite-time transients than the corresponding linear response current correlators; thus, new parameter regimes can become accessible. As an application, we determine the thermal Drude weight of the Hubbard model for temperatures T which are an order of magnitude smaller than those reached in the equilibrium approach. This allows us to demonstrate that at low T and half filling, thermal transport is successively governed by spin excitations and described quantitatively by the Bethe ansatz Drude weight of the Heisenberg chain.

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• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Superdiffusion in spin chains
• Ballistic spin transport in a periodically driven integrable quantum system
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Emergent tracer dynamics in constrained quantum systems
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Popcorn Drude weights from quantum symmetry
• Thermal conductivity and heat diffusion in the two-dimensional Hubbard model
• Ballistic transport in integrable quantum chains with degenerate spectra
• Non-equilibrium boundary driven quantum systems: models, methods and properties