An exact and explicit ladder-tensor-network ansatz is presented for the nonequilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges of the chain only. We show that the steady-state density operator of a finite system of size n is—apart from a normalization constant—a polynomial of degree 2n - 2 in the coupling constant. Efficient computation of physical observables is facilitated in terms of a transfer operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n^2 scaling of the spin current, and long-range correlations in the steady state. This is a fully nonperturbative extension of a recent result [Phys. Rev. Lett. 106, 217206 (2011)]
COBISS.SI-ID: 2381668
An explicit matrix product ansatz is presented, in the first two orders in the (weak) coupling parameter, for the nonequilibrium steady state of the homogeneous, nearest neighbor Heisenberg XXZ spin 1/2 chain driven by Lindblad operators which act only at the edges of the chain. The first order of the density operator becomes in the thermodynamic limit an exact pseudolocal conservation law and yields -- via the Mazur inequality -- a rigorous lower bound on the high-temperature spin Drude weight. Such a Mazur bound is found a nonvanishing fractal function of the anisotropy parameter Delta for Delta less than 1.
COBISS.SI-ID: 2347108
We find that non-equilibrium boundary conditions generically trigger long range order in non-equilibrium steady states of locally but strongly interacting quantum chains. We treated models quantum spin 1/2 chains which are driven far from equilibrium by coupling to a pair Lindblad reservoirs attached to the ends of the chain. In particular, we find a phase transition from exponentially decaying to long range spin-spin correlations in integrable Heisenberg XXZ chain by changing the anisotropy parameter. Long range order also typically emerges after breaking the integrability of the model.
COBISS.SI-ID: 2262884
We study a new class of quantum chaotic systems with dynamical localization, where gain/loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value gamma_PT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for gamma_PT, and show that chaos assists the exact PT-phase. Our results have applications to the design of active optical elements with PT-symmetry.
COBISS.SI-ID: 2234724
Time dependent density matrix renormalization group method with matrix product ansatz has been employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum chains, which are driven far from equlibrium by means of Markovian couplings to external baths at the two ends. 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 with up to 100 spins.
COBISS.SI-ID: 2150756