Non-Equilibrium Steady States in Quantum Spin Chains

A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time evolution cannot be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, with the result that chains of length of the order of n≈100 spins are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. A previously conjectured relation between quantum chaos and normal transport is re-confirmed with high accuracy for much larger systems.A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time evolution cannot be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, with the result that chains of length of the order of n≈100 spins are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. A previously conjectured relation between quantum chaos and normal transport is re-confirmed with high accuracy for much larger systems.

arXiv:0811.4188Journal of Statistical Mechanics Theory and ExperimentFeb 1, 2009239 citations

Matrix product simulations of non-equilibrium steady states of quantum spin chains

Tomaž Prosen

Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.

Jan 1, 2008216 citations

Dynamic properties of quantum spin chains

Joachim Stolze, Taras Verkholyak, Oleg Derzhko +1 more

Oct 15, 20076 citations

Non-equilibrium steady states of the boundary-driven Heisenberg quantum spin chain

Gunter Markus Schutz

We consider an open Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. We derive a matrix product ansatz for the non-equilibrium density matrix. For the isotropic chain we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady steady state of a chain with $N$ sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle $\theta$ . The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady state currents scale as $1/N^{2}$ for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to $2\theta/N$ .We consider an open Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. We derive a matrix product ansatz for the non-equilibrium density matrix. For the isotropic chain we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady steady state of a chain with $N$ sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle $\theta$. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady state currents scale as $1/N^{2}$ for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to $2\theta/N$.

Jan 1, 20150 citations

Finitely correlated states on quantum spin chains

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

Communications in Mathematical PhysicsMar 1, 19921,418 citations

N

sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle

\theta

. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady state currents scale as

1/N^{2}

for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to

2\theta/N