Lower bounds for the conductivities of correlated quantum systems

Abstract

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.

Title changed; 9 pages, 2 figures

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Cited by in corpus (33)

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• Theory of hydrodynamic transport in fluctuating electronic charge density wave states
• Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder
• DC resistivity at the onset of spin density wave order in two-dimensional metals
• Conductivity of a strange metal: from holography to memory functions
• Spin conductivity in almost integrable spin chains
• Pumping approximately integrable systems
• Large violation of Wiedemann Franz law in Luttinger liquids
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• The Luttinger liquid and integrable models
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
• Thermal transport in one-dimensional spin heterostructures
• Scaling of electrical and thermal conductivities in an almost integrable chain
• Field-dependent thermal transport in the Haldane chain compound NENP
• Superdiffusive transport of energy in one-dimensional metals
• Quantum bounds on heat transport through nanojunctions
• Heat transport of clean spin-ladders coupled to phonons: Umklapp scattering and drag
• Holographic incoherent transport in Einstein-Maxwell-dilaton Gravity
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Thermal conductivity at a disordered quantum critical point
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule
• Multiple relaxation times in perturbed XXZ chain
• Large thermomagnetic effects in weakly disordered Heisenberg chains
• Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap
• Demystifying the Holographic Mystique
• Magnetothermal Transport in Spin-Ladder Systems
• Einstein relation for subdiffusive relaxation in Stark chains