We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length ℓ . We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length ℓ . We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.

arXiv:2002.04367Europhysics Letters (EPL)Apr 28, 202086 citations

On form-factor expansions for the XXZ chain in the massive regime

Maxime Dugave, Frank Göhmann, Karol Kajetan Kozlowski +1 more

We study the large-volume- L limit of form factors of the longitudinal spin operators for the XXZ spin-1/2 chain in the massive regime. We find that the individual form factors decay as L − n , n being an even integer counting the number of physical excitations—the holes—that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin–spin correlation functions in the thermodynamic limit L → +∞. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.We study the large-volume- L limit of form factors of the longitudinal spin operators for the XXZ spin-1/2 chain in the massive regime. We find that the individual form factors decay as L − n , n being an even integer counting the number of physical excitations—the holes—that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin–spin correlation functions in the thermodynamic limit L → +∞. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.

arXiv:1412.8217Journal of Statistical Mechanics Theory and ExperimentMay 28, 201529 citations

Anomalous transport in spin chains

Vipin Kerala Varma, Vadim Oganesyan, Antonello Scardicchio +2 more

Bulletin of the American Physical SocietyMar 9, 20180 citations

Finite-temperature transport in the gapped spin- 1 2 XXZ chain and one-dimensional lattice spinless fermion model

J. M. P. Carmelo, Pedro D Sacramento

It is well established that at zero magnetic field $h=0$ , the spin diffusion constant of the spin- $\frac{1}{2}$ XXZ chain is for anisotropy $\mathrm{\ensuremath{\Delta}}>1$ finite for both low and high temperatures, implying that the type of spin transport is normal diffusive. Although it is expected that this holds for all finite temperatures $T>0$ , the calculation of the spin diffusion constant for all $T$ is typically intractable. Here we consider a class of energy eigenstates that exist both for anisotropies $\mathrm{\ensuremath{\Delta}}=1$ and $\mathrm{\ensuremath{\Delta}}>1$. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for $T>0$ . That for $\mathrm{\ensuremath{\Delta}}>1$ such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for $T>0$ . By combining the connection through a Jordan-Wigner transformation of the spin- $\frac{1}{2}$ XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential $\ensuremath{\mu}=0$, for $V/J\ensuremath{\ge}1$ with its Bethe-ansatz solution, where $V$ is the nearest-neighbor Coulomb repulsion and $J=2t$ is twice the hopping integral $t$ , in this paper we also address the issue of the $T>0$ charge transport of that model at $\ensuremath{\mu}=0$. It is found to be anomalous superdiffusive for $V/J=1$ and normal diffusive for $V/J>1$ . Our results thus open the door to a key advance in the understanding for all finite temperatures $T>0$ of the spin transport in the spin- $\frac{1}{2}$ XXZ chain at $h=0$ for anisotropy $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}1$ and of the charge transport in the 1D lattice spinless fermion model at $\ensuremath{\mu}=0$ for $V/J\ensuremath{\ge}1$.It is well established that at zero magnetic field $h=0$, the spin diffusion constant of the spin-$\frac{1}{2}$ XXZ chain is for anisotropy $\mathrm{\ensuremath{\Delta}}>1$ finite for both low and high temperatures, implying that the type of spin transport is normal diffusive. Although it is expected that this holds for all finite temperatures $T>0$, the calculation of the spin diffusion constant for all $T$ is typically intractable. Here we consider a class of energy eigenstates that exist both for anisotropies $\mathrm{\ensuremath{\Delta}}=1$ and $\mathrm{\ensuremath{\Delta}}>1$. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for $T>0$. That for $\mathrm{\ensuremath{\Delta}}>1$ such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for $T>0$. By combining the connection through a Jordan-Wigner transformation of the spin-$\frac{1}{2}$ XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential $\ensuremath{\mu}=0$, for $V/J\ensuremath{\ge}1$ with its Bethe-ansatz solution, where $V$ is the nearest-neighbor Coulomb repulsion and $J=2t$ is twice the hopping integral $t$, in this paper we also address the issue of the $T>0$ charge transport of that model at $\ensuremath{\mu}=0$. It is found to be anomalous superdiffusive for $V/J=1$ and normal diffusive for $V/J>1$. Our results thus open the door to a key advance in the understanding for all finite temperatures $T>0$ of the spin transport in the spin-$\frac{1}{2}$ XXZ chain at $h=0$ for anisotropy $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}1$ and of the charge transport in the 1D lattice spinless fermion model at $\ensuremath{\mu}=0$ for $V/J\ensuremath{\ge}1$.

arXiv:2509.08741Physical review. B./Physical review. BAug 26, 20253 citations

It is well established that at zero magnetic field

h=0

, the spin diffusion constant of the spin-

\frac{1}{2}

XXZ chain is for anisotropy $\mathrm{\ensuremath{\Delta}}>1$ finite for both low and high temperatures, implying that the type of spin transport is normal diffusive. Although it is expected that this holds for all finite temperatures

T>0

, the calculation of the spin diffusion constant for all

T

is typically intractable. Here we consider a class of energy eigenstates that exist both for anisotropies $\mathrm{\ensuremath{\Delta}}=1$ and $\mathrm{\ensuremath{\Delta}}>1$. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for

T>0

. That for $\mathrm{\ensuremath{\Delta}}>1$ such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for

T>0

. By combining the connection through a Jordan-Wigner transformation of the spin-

\frac{1}{2}

XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential $\ensuremath{\mu}=0$, for $V/J\ensuremath{\ge}1$ with its Bethe-ansatz solution, where

V

is the nearest-neighbor Coulomb repulsion and

J=2t

is twice the hopping integral

t

, in this paper we also address the issue of the

T>0

charge transport of that model at $\ensuremath{\mu}=0$. It is found to be anomalous superdiffusive for

V/J=1

and normal diffusive for

V/J>1

. Our results thus open the door to a key advance in the understanding for all finite temperatures

T>0

of the spin transport in the spin-

\frac{1}{2}

XXZ chain at

h=0

for anisotropy $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}1$ and of the charge transport in the 1D lattice spinless fermion model at $\ensuremath{\mu}=0$ for $V/J\ensuremath{\ge}1$.