My main research interest is the non-equilibrium behavior of quantum many-body systems. In the past decades, condensed matter theory has mainly focused on understanding the equilibrium or linear response properties of condensed matter systems. Recent experimental advances in ultracold gases, nanostructures and pump-probe spectroscopy have opened up the exciting new field of non-equilibrium quantum many-body physics with many fundamental questions like thermalization in isolated systems, the role of integrability in non-equilibrium dynamics, physics beyond the linear response regime, etc. This has led to a lot of activity and my group is pursuing these questions using mainly analytical tools supplemented with numerical methods. We are also interested in developing new theoretical methods inspired by AdS/CFT correspondence, that is the duality between certain strong-coupling quantum field theories and geometrodynamcis like Einstein's theory of general relativity.
This is a link to an overview talk about non-equilibrium dynamics that I gave at the KITP.
Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition
|The Hall conductance as a function of (Mf,Bf) for different (Mi,Bi).|
We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying linear response theory to the diagonal ensemble. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap m_f in the post-quench Hamiltonian H_f. The topological invariant for the quenched state is the winding number of the Green's function W, which equals the Chern number for the ground state of H_f. In the limit that m_f goes to zero, the derivative of the Hall conductance with respect to m_f is proportional to ln(|m_f|), with the constant of proportionality being the ratio of the change of W at m_f = 0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis. [more...]
Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
|Rate function for a double quench from g = 0.5 to g|
The recently discovered dynamical phase transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper we extend the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T>0. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. [more...]
Representation of excited states and topological order of the toric code in MERA
|The holographic contribution to the topological entanglement entropy on different scales.|
The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured that the tensor networks which arise during the real space renormalization procedure like the multi-scale entanglement renormalization ansatz (MERA) are a discretized version of the background of the gravity theory. We conside an explicit and tractable example, namely the dual network of the toric code, for which MERA can be performed analytically even for excited states. Furthermore, we show how to calculate topological entanglement entropy from the geometry of MERA. [more...]
Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
|Distribution of zeros of the Loschmidt echo in the complex time plane for two different quenches. The zeros form areas in the complex plane .|
The notion of a dynamical quantum phase transition (DQPT) was recently introduced as the non-analytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model are studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS-type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the non-degenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model. [more...]