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Bulletin of the American Physical Society

Coherence and a quench dynamics of a dissipative quantum system: renormalization group and dynamical phases

Oleksiy Kashuba

Published Mar 3, 2014• 0 citations
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We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subject to an abrupt quench in the parameters of the underlying Hamiltonian is investigated using two complementary renormalization group approaches. The methods are applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory for the relaxation before and after the quench of the spin-boson coupling and the Zeeman splitting of the up and down spin is investigated.
A renormalization group approach is used to show that a one-dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light cone increases as a nonanalytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time dependent, crucially affecting the time evolution of the system. Explicit results are presented for the time evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.
The global quench dynamics of 3-state quantum Potts spin chain is investigated for different initial states using quantum renormalization group method. The results show that the value of negativity is maximum or minimum at quantum phase transition point and the steady value of negativity is also dependent on the initial states, which means that the dynamic behavior is strongly dependent on the initial states. The range of negativity is decreases as the size of system increases for different steps of renormalization group transformations.