Zero-temperature dynamics of the one-dimensional XXZ and t-J models

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

Low energy excitations of the t-J model in one and two dimensions

T. K. Lee, R. Eder, Y. C. Chen +3 more

APSMar 1, 19970 citations

Exact Dynamics of One-Dimensional t-J Model with Long-Range Interaction

Yasuhiro Saiga, Mitsuhiro Arikawa, Yoshio Kuramoto

JJAP seriesFeb 8, 19990 citations

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

Kiyoto Nakamura, Yoshitaka Tanimura

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.

arXiv:2111.13277The Journal of Chemical PhysicsNov 30, 20219 citations

Phase diagram of the one-dimensional t−J model

K. Hallberg, C. A. Balseiro

Solid State CommunicationsMay 1, 19926 citations

Large bond-dimension time-evolution block decimation study of the XXZ quantum spin chains of S = 1/2 and 1

Hwan Bin Choi, Ji-Woo Lee

We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.

Journal of the Korean Physical SocietySep 1, 20173 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 $V/J\ensuremath{\ge}1$.