Quantum Quenches in Chern Insulators.

We explore the nonequilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and nontopological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.This work was supported by EPSRC Grants EP/J017639/1 and EP/K030094/1. MJB thanks the EPSRC Centre for Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES) funded under grant EP/L015854/1. MJB and MDC thank the Thomas Young Center.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevLett.115.23640

Hall response and edge current dynamics in Chern insulators out of equilibrium

We investigate the transport properties of Chern insulators following a quantum quench between topological and non-topological phases. Recent works have shown that this yields an excited state for which the Chern number is preserved under unitary evolution. However, this does not imply the preservation of other physical observables, as we stressed in our previous work. Here we provide an analysis of the Hall response following a quantum quench in an isolated system, with explicit results for the Haldane model. We show that the Hall conductance is no longer related to the Chern number in the post-quench state, in agreement with previous work. We also examine the dynamics of the edge currents in finite-size systems with open boundary conditions along one direction. We show that the late-time behavior is captured by a Generalized Gibbs Ensemble, after multiple traversals of the sample. We discuss the effects of generic open boundary conditions and confinement potentials.Engineering and Physical Sciences Research Council (Grant IDs: EP/J017639/1, EP/K030094/1, EP/L015854/1), Thomas Young CenterThis is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevB.94.15510

Transport fluctuations in integrable models out of equilibrium

We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We do this by combining insights from generalised hydrodynamics with a theory of large deviations in ballistic transport. The results are applicable to a wide variety of physical systems, including the Lieb-Liniger gas and the Heisenberg chain. We confirm the predictions in non-equilibrium steady states obtained by the partitioning protocol, by comparing with Monte Carlo simulations of this protocol in the classical hard rod gas. We verify numerically that the exact results obey the correct non-equilibrium fluctuation relations with the appropriate initial conditions.Comment: v1: 7 + 8 pages, 6 figures. v2: 32 pages, format and discussion improved. v3: typo in the formula for c4 corrected. v4: 33 pages, discussion further improve

Topological marker currents in Chern insulators

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment

Magnetothermoelectric response at a superfluid-Mott-insulator transition

We investigate the finite temperature magnetothermoelectric response in the vicinity of a superfluid-Mott-insulator quantum phase transition. We focus on the particle-hole symmetric transitions of the Bose-Hubbard model, and combine Lorentz invariance arguments with quantum Boltzmann calculations. By means of an epsilon expansion, we find that a nonvanishing thermoelectric tensor and a finite thermal transport coefficient are supported in this quantum critical regime. We comment on the singular Nernst effect in this problem

Magnetothermoelectric response at a superfluid-mott-insulator transition (vol 98, art no 166801, 2007)

Publisher’s Note: Magnetothermoelectric Response at a Superfluid–Mott-Insulator Transition [Phys. Rev. Lett. 98, 166801 (2007)