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Journal of Physics Communications

Energy current and Casimir effect with phase transition in the nonequilibrium steady-state of a quantum anisotropic XY spin chain

Georges Collince Fouokeng, F. Kuate Fodouop, Martin Tchoffo, Lukong Cornelius Fai, E B Ngompe Nkouankam

Published Jan 22, 2019• 0 citations

Abstract

The dynamics of quantum anisotropic XY spin chain driven out of equilibrium by a transverse magnetic field, that carry an energy current ( J E ) is investigated. Considering the spin exchange and the flow of energy trapped in magnetic field between two defects in the x y -plane separated by a distance d , we derive an analytical expression of the steady state Green's function of the model using the Grassmann algebra in order to determine the Casimir force between two magnetic defects. As soon as done we find that, cooling the system as well as increasing the anisotropic parameter decrease the energy current and accordingly increase the range of the Casimir force. This symmetry is broken with a significant increase of distance between the defects. A critical temperature is then recorded exhibiting a phase transition according to the anisotropic parameter. An interesting feature of this model is that turning the anisotropic parameter as well as the temperature range will better manipulate the energy flux and control the range of the Casimir force.

DOI: 10.1088/2399-6528/ab0047

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The dynamics of quantum anisotropic XY spin chain driven out of equilibrium by a transverse magnetic field, that carry an energy current ( J E ) is investigated. Considering the spin exchange and the flow of energy trapped in magnetic field between two defects in the x y -plane separated by a distance d , we derive an analytical expression of the steady state Green's function of the model using the Grassmann algebra in order to determine the Casimir force between two magnetic defects. As soon as done we find that, cooling the system as well as increasing the anisotropic parameter decrease the energy current and accordingly increase the range of the Casimir force. This symmetry is broken with a significant increase of distance between the defects. A critical temperature is then recorded exhibiting a phase transition according to the anisotropic parameter. An interesting feature of this model is that turning the anisotropic parameter as well as the temperature range will better manipulate the energy flux and control the range of the Casimir force.

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely, an energy-flux-driven quantum

\mathit{XX}

chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux-carrying steady state.

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We obtain the steady-state phase diagram of a transverse-field XY spin chain coupled at its ends to magnetic reservoirs held at different magnetic potentials. In the long-time limit, the magnetization bias across the system generates a current-carrying nonequilibrium steady state. We characterize the different nonequilibrium phases as functions of the chain's parameters and magnetic potentials, in terms of their correlation functions and entanglement content. The mixed-order transition, previously observed for the case of a transverse-field Ising chain, is established to emerge as a generic feature of a wider class of out-of-equilibrium problems. The critical exponents associated with this universality class are determined analytically. Results are also contrasted with those obtained in the limit of Markovian reservoirs. Our findings should prove helpful in establishing the properties of nonequilibrium phases and phase transitions of extended open quantum systems.

We study the nonequilibrium steady states of an Ising chain in a transverse field

h

by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature,

h

- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.

The spin-1/2 quantum anisotropic XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.

The zero-temperature phase diagram of a quasiperiodic anisotropic

\mathrm{XY}

quantum spin chain in a transverse magnetic field is studied. In the isotropic limit, the system exhibits an infinite number of quantum phase transitions with a devil's-staircase-like magnetization curve. Anisotropy decreases the number of transitions. A mechanism is proposed for the successive transitions based on the ordering of finite clusters of spins along the chain.