Absence of high-temperature ballistic transport in the spin-$1/2$ $XXX$ chain within the grand-canonical ensemble

Abstract

Whether in the thermodynamic limit, vanishing magnetic field $h\to 0$, and nonzero temperature the spin stiffness of the spin-$1/2$ $XXX$ Heisenberg chain is finite or vanishes within the grand-canonical ensemble remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an upper bound on the stiffness and show that within that ensemble it vanishes for $h\to 0$ in the thermodynamic limit of chain length $L\to \infty$, at high temperatures $T\to \infty$. Our approach uses a representation in terms of the $L$ physical spins $1/2$. For all configurations that generate the exact spin-$S$ energy and momentum eigenstates such a configuration involves a number $2S$ of unpaired spins $1/2$ in multiplet configurations and $L-2S$ spins $1/2$ that are paired within $M_{\mathrm{sp}}=L/2-S$ spin-singlet pairs. The Bethe-ansatz strings of length $n=1$ and $n>1$ describe a single unbound spin-singlet pair and a configuration within which $n$ pairs are bound, respectively. In the case of $n>1$ pairs this holds both for ideal and deformed strings associated with $n$ complex rapidities with the same real part. The use of such a spin $1/2$ representation provides useful physical information on the problem under investigation in contrast to often less controllable numerical studies. Our results provide strong evidence for the absence of ballistic transport in the spin-$1/2$ $XXX$ Heisenberg chain in the thermodynamic limit, for high temperatures $T\to \infty$, vanishing magnetic field $h\to 0$ and within the grand-canonical ensemble.

References in corpus (26)

• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Diffusion and ballistic transport in one-dimensional quantum systems
• Families of quasi-local conservation laws and quantum spin transport
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Spin-current autocorrelations from single pure-state propagation
• On the finite temperature Drude weight of the anisotropic Heisenberg chain
• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Low-temperature transport in Heisenberg chains
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Anomalous scaling of conductivity in integrable fermion systems
• The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Signatures of integrability in charge and thermal transport in 1D quantum systems
• Curvature of Levels and Charge Stiffness of One-Dimensional Spinless Fermions
• Finite-Temperature Transport in Finite-Size Hubbard Rings in the Strong-Coupling Limit
• Large N behavior of string solutions in the Heisenberg model
• Nonlocal spin transport in single walled carbon nanotube networks
• Low-energy spin dynamics in the [YPc2]0 S=1/2 antiferromagnetic chain
• Charge and Spin Transport in the One-dimensional Hubbard Model
• Dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

Cited by in corpus (14)

• Microscopic origin of ideal conductivity in integrable quantum models
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Interacting and noninteracting integrable systems
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit
• Anomalous and regular transport in spin 1/2 chains: AC conductivity
• Pseudoparticle approach to 1D integrable quantum models
• Absence of ballistic charge transport in the half-filled 1D Hubbard model
• Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain
• Finite-temperature charge and spin transport in the one-dimensional Hubbard model accounting for its global [SU (2) X SU(2) X U(1)]/Z_2^2$ symmetry
• Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it
• The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
• Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm