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DY: Fachverband Dynamik und Statistische Physik

DY 31: Quantum dynamics, decoherence and quantum information

DY 31.10: Vortrag

Freitag, 29. Februar 2008, 12:30–12:45, MA 004

Bypassing the quantum phase transition for the Ising model in a transverse field — •Gernot Schaller — Institut für Theoretische Physik, Technische Universität Berlin

The one-dimensional quantum Ising model describes a spin-1/2 chain coupled by ferromagnetic 1d next-neighbor interactions subject to a transverse magnetic field. It is a paradigmatic example for an analytically solvable model that exhibits a second order quantum phase transition in the continuum limit from a phase with a unique ground state to a two-fold degenerate ground state with a spontaneously broken symmetry.

For a system with n spins and a merely time-dependent external magnetic field, this is reflected in a O(1/n)-scaling of the energy gap at the critical point between ground state and first excited state. However, the situation becomes different if one considers a spatially inhomogeneous magnetic field. For a special configuration one can demonstrate analytically that the energy gap in the relevant subspace is bounded from below by a constant independent of the system size. Likewise, the ground state does not change drastically at some critical point anymore. The dynamics through this transition will be compared with the original model in the adiabatic limit.