We use fidelity to characterize the information about a quantum state contained in another quantum state. In a multi-qubit system, each qubit has individual information about a prescribed quantum state. We investigate how the total information changes under the interactions of nonlocal Hamiltonians. We show that for some special physical interactions the total information is conserved. This type of nonlocal Hamiltonians are named as Conservative Hamiltonians, similar to the Conservative Forces. We then apply this Information Conservation Law in the quantum spin system, and propose methods for improving the efficiency of quantum communications through an open end spin chain.We use fidelity to characterize the information about a quantum state contained in another quantum state. In a multi-qubit system, each qubit has individual information about a prescribed quantum state. We investigate how the total information changes under the interactions of nonlocal Hamiltonians. We show that for some special physical interactions the total information is conserved. This type of nonlocal Hamiltonians are named as Conservative Hamiltonians, similar to the Conservative Forces. We then apply this Information Conservation Law in the quantum spin system, and propose methods for improving the efficiency of quantum communications through an open end spin chain.

Jul 4, 20050 citations

Quantum spin chains with lattice supersymmetry

Junye Yang

Jan 1, 20180 citations

Spin Chains with Dynamical Lattice Supersymmetry

Christian Hagendorf

arXiv:1207.0357Journal of Statistical PhysicsFeb 1, 201331 citations

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

Peter Jung, R. W. Helmes, Achim Rosch

The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin- $1/2$ nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-$1/2$ nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.

arXiv:cond-mat/0509615Physical Review LettersFeb 14, 2006123 citations

Spin conductivity in almost integrable spin chains

Peter Jung, Achim Rosch

The spin conductivity in the integrable spin- $1∕2$ $XXZ$ chain is known to be infinite at finite temperatures $T$ for anisotropies $\ensuremath{-}1<\ensuremath{\Delta}<1$. Perturbations, which break integrability, e.g., a next-nearest neighbor coupling ${J}^{\ensuremath{'}}$, render the conductivity finite. We construct numerically a nonlocal conserved operator ${J}_{\ensuremath{\parallel}}$ which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small ${J}^{\ensuremath{'}}$. This allows us to obtain a lower bound for the spin conductivity ${\ensuremath{\sigma}}_{s}\ensuremath{\geqslant}c(T)∕{{J}^{\ensuremath{'}}}^{2}$, where $c(T)$ is finite for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}0$. We discuss the implication of our result for the general question how nonlocal conservation laws affect transport properties.The spin conductivity in the integrable spin-$1∕2$ $XXZ$ chain is known to be infinite at finite temperatures $T$ for anisotropies $\ensuremath{-}1<\ensuremath{\Delta}<1$. Perturbations, which break integrability, e.g., a next-nearest neighbor coupling ${J}^{\ensuremath{'}}$, render the conductivity finite. We construct numerically a nonlocal conserved operator ${J}_{\ensuremath{\parallel}}$ which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small ${J}^{\ensuremath{'}}$. This allows us to obtain a lower bound for the spin conductivity ${\ensuremath{\sigma}}_{s}\ensuremath{\geqslant}c(T)∕{{J}^{\ensuremath{'}}}^{2}$, where $c(T)$ is finite for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}0$. We discuss the implication of our result for the general question how nonlocal conservation laws affect transport properties.

arXiv:0708.1313Physical Review BDec 7, 200771 citations

The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-

1/2

nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.

The spin conductivity in the integrable spin-

1∕2

XXZ

chain is known to be infinite at finite temperatures

T

for anisotropies $\ensuremath{-}1<\ensuremath{\Delta}<1$. Perturbations, which break integrability, e.g., a next-nearest neighbor coupling ${J}^{\ensuremath{'}}$, render the conductivity finite. We construct numerically a nonlocal conserved operator ${J}_{\ensuremath{\parallel}}$ which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small ${J}^{\ensuremath{'}}$. This allows us to obtain a lower bound for the spin conductivity ${\ensuremath{\sigma}}_{s}\ensuremath{\geqslant}c(T)∕{{J}^{\ensuremath{'}}}^{2}$, where

c(T)

is finite for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}0$. We discuss the implication of our result for the general question how nonlocal conservation laws affect transport properties.