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

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 transverse 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, i.e. they do not decay to the ground states. We also discuss the decoherence dynamics for an initial state formed by a quantum superposition of the two degenerate ground states corresponding to the orthogonal classical, ferromagnetic states. arXiv:1804.07559v2 [cond-mat.str-el]

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“…The coherence decay is introduced using the Lindblad equation [22] with the jump operator being in the form [23]:…”

Dissipation in spin chains using quantized nonequilibrium thermodynamics

“…In this, respect, lattice models such as Heisenberg and Hubbard [7,8] are paramount examples of many-body dissipation [9,10]. The general framework within which these investigations are typically conducted is that of Markovian master equations in the standard Lindblad form and it has been applied to both driven and autonomous systems [11][12][13]. For a recent review, see [14].…”

Decoherence and relaxation of topological states in extended quantum Ising models

“…More recently, the quantum Ising model was studied in the non-equilibrium regime to investigate the dynamical behavior of quantum phase transitions, e.g. the quenching in a driven Ising chain [13][14][15][16][17][18], the Kibble-Zurek mechanism [19,20], the Loschmidt echo of a single impurity coupled to the Ising chain [21], the engineered quantum transfer [22], the quantum superposition of topological defects [23], the decoherence dynamics in the strong coupling regime [24] as well as the role of quantum correlations in quantum phase transitions [25][26][27]. Importantly, the generalized class of Ising models can be characterized by a topological number [28][29][30][31][32] and, in the topologically nontrivial phase, localized states can occur at the end of an open chain [1,4] or at the interface separating regions with different topological number [33].…”

“…More recently, the quantum Ising model was studied in the non-equilibrium regime to investigate the dynamical behavior of quantum phase transitions, e.g. the quenching in a driven Ising chain [13][14][15][16][17][18], the Kibble-Zurek mechanism [19,20], the Loschmidt echo of a single impurity coupled to the Ising chain [21], the engineered quantum transfer [22], the quantum superposition of topological defects [23], the decoherence dynamics in the strong coupling regime [24] as well as the role of quantum correlations in quantum phase transitions [25][26][27].…”

“…This model of longitudinal dissipation was considered to address the quantum phase transition using the mean field approximation [73] or an exact approach based on path integral [74]. This kind of dissipation was also analyzed to investigate dynamical phase transitions [75][76][77][78], non-equilibrium states in presence of temperature differences [79], quantum diffusion [80] and relaxation dynamics in the strong coupling limit [24].…”