Universal nonequilibrium quantum dynamics in imaginary time

Details Universal nonequilibrium quantum dynamics in imaginary time Universal nonequilibrium quantum dynamics in imaginary time

2011-06-21

arxiv.org/abs/1106.4078v4

Phys. Rev. B 84, 224303 (2011)

Physics

Condensed Matter

Other Condensed Matter

8 pages, 3 figures. Expanded, final published version

Scientific paper

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.

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