Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains

Abstract

We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero -- and thus transport is dissipationless -- everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Spectral functions in one-dimensional quantum systems at T>0
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Spin conductivity in almost integrable spin chains
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain
• Finite Drude weight for 1D low temperature conductors

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