1106.4078 (C. De Grandi et al.)

Universal nonequilibrium quantum dynamics in imaginary time    [PDF]

C. De Grandi, A. Polkovnikov, A. W. Sandvik

We propose a method to study dynamical response of a quantum system by
evolving it with an imaginary-time dependent Hamiltonian. The leading
non-adiabatic response of the system driven to a quantum-critical point is
universal and characterized by the same exponents in real and imaginary time.
For a linear quench protocol, the fidelity susceptibility and the geometric
tensor naturally emerge in the response functions. Beyond linear response, we
extend the finite-size scaling theory of quantum phase transitions to
non-equilibrium setups. This allows, e.g., for studies of quantum phase
transitions in systems of fixed finite size by monitoring expectation values as
a function of the quench velocity. Non-equilibrium imaginary-time dynamics is
also amenable to quantum Monte Carlo (QMC) simulations, with a scheme that we
introduce here and apply to quenches of the transverse-field Ising model to
quantum-critical points in one and two dimensions. The QMC method is generic
and can be applied to a wide range of models and non-equilibrium setups.

View original: http://arxiv.org/abs/1106.4078