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arXiv:1804.07559 · Physical Review A

Decoherence in the quantum Ising model with transverse dissipative interaction in the strong-coupling regime

Hannes Weisbrich, C. Saussol, Wolfgang Belzig, Gianluca Rastelli

Published Nov 7, 2018• 12 citations
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Abstract

We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely, the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong-coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, namely, they do not decay to the ground states.

DOI
10.1103/physreva.98.052109

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We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely, the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong-coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, namely, they do not decay to the ground states.
We study the decoherence and the relaxation dynamics of topological states in an extended class of quantum Ising chains which can present a multidimensional ground state subspace. The leading interaction of the spins with the environment is assumed to be the local fluctuations of the transverse magnetic field. By deriving the Lindblad equation using the many-body states, we investigate the relation between decoherence, energy relaxation and topology. In particular, in the topological phase and at low temperature, we analyze the dephasing rates between the different degenerate ground states.
We study the decoherence of a qubit weakly coupled to frustrated spin baths. We focus on spin baths described by the classical Ising spin glass and the quantum random transverse Ising model which are known to have complex thermodynamic phase diagrams as a function of an external magnetic field and temperature. Using a combination of numerical and analytical methods, we show that for baths initially in thermal equilibrium, the resulting decoherence is highly sensitive to the nature of the coupling to the environment and is qualitatively different in different parts of the phase diagram. We find an unexpected strong non-Markovian decay of the coherence when the random transverse Ising model bath is prepared in an initial state characterized by a finite temperature paramagnet. This is contrary to the usual case of exponential decay (Markovian) expected for spin baths in finite temperature paramagnetic phases, thereby illustrating the importance of the underlying nontrivial dynamics of interacting quantum spinbaths.
To create a more comprehensive understanding of nonequilibrium dynamics of open quantum many-body systems, we visit an exactly solvable example, that is a quenched transverse-field Ising chain coupled to Markovian baths, which act locally on the Jordan-Wigner fermionic space. Performing explicit calculations on the heat transfer, transverse magnetization, and kink density, we find that the imbalance of two opposite damping mechanisms play a crucial role in constructing a nontrivial nonequilibrium steady state accompanied with a dissipative quantum phase transition, also that the competition between unitary drive and decoherence does not necessarily lead to a quasi-stationary state or prethermalization under certain ordinary relaxation.
We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and nonadiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence makes it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline antibunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.
We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase diagram of the latter is calculated as a function of coupling to the heat bath and the transverse magnetic field. Collective excitations at low temeratures are assessed within a spin-wave like analysis that exhibits a vanishing energy gap at the quantum critical point. We also consider another limit where the system reduces to a generalized spin-boson model of two interacting spins. By increasing the coupling strength with the heat bath, the two-spin wavefunction changes from an entangled state to a factorized state of two spins which are aligned along the transverse field. We also discuss the possible realization and application of the model to different physical systems.
We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for the discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2S2S2S nonintersecting zones.