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Universal non-equilibrium imaginary time dynamics

Anatoli Polkovnikov

22.06.2011 at 12:45 

I will discuss a new method of studying a slow dynamical response of a quantum system by analyzing its imaginary

time evolution under a time-evolving Hamiltonian. This setup bears a lot of similarities with the real-time

quantum dynamics. In particular, the leading non-adiabatic response of the system driven to a quantum critical

point is universal and is characterized by the same critical exponents and similar scaling functions as for the

real time protocol. I will discuss a linear response theory in a non-adiabatic parameter like velocity of the

quench and define the corresponding susceptibilities. The advantage of the imaginary time dynamics is that it is

amenable to Quantum Monte Carlo simulations allowing one to analyze a wide class of quantum systems. I will

mention work in progress on application of this scheme for Monte-Carlo simulations of the imaginary time quantum

annealing. I will illustrate general results by specific example of quenching to the quantum critical points in

the transverse field Ising model.

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