Dissipative Quantum Disordered Models

Abstract

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -glassy -phase from the disordered phase that, for some longrange interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.

Out-of-equilibrium dynamics of classical and quantum complex systems

“…In spin models on hyper-random graphs with finite or infinite connectivity and multi-spin interactions the random first order phase transition becomes a genuine first order one at low temperatures [62]. This fact has formidable consequences to the failure of quantum annealing methods to solve hard optimisation problems that can be mapped, as already mentioned in Sec.…”

“…The out of equilibrium relaxation of these systems coupled to a quantum environment, for a generic initial density matrix not correlated with the quenched randomness hence mimicking a quench from the disordered phase, can be investigated with the Schwinger-Keldysh closed-time formalism. For details on these calculations see [62] and references therein. Even more so than in the classical case, going beyond mean-field is extremely hard.…”

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

“…Then the interaction and the coupling to the bath can still have the same direction for α = β = x but they can be both orthogonal to the transverse field. In this situation of parallel dissipation, the phase diagram was explored using quantum Montecarlo simulations [26][27][28][29]. Since the interaction operator and dissipative coupling operator commute, the result in the phase diagram is that the stronger the coupling with the environment is, the larger is the ordered phase region (the ferromagnetic phase), namely the critical ratio for J/B for the quantum phase transition decreases with the dissipation.…”

“…Numerical quantum Montecarlo simulations were employed to unveil the phase diagram of a dissipative quantum Ising lattice with Ohmic dissipation [26][27][28][29]. Effects of the disorder were analyzed using a renormalization group approach [30].…”

“…The effects of the dissipation can depend crucially on the operators coupling to the bath. In the works [26][27][28][29][30], each spin was coupled to the environment through the same spin direction of the spin-spin interaction. However, the dissipative coupling of the 1D Ising chain with the environment can occur even through other directions.…”