# Persistent Hall response after a quantum quench

Reference: arXiv:1603.01621

# Abstract

Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here we unveil how out-of-equilibrium states, prepared via a quantum quench, can exhibit a non-zero Hall-type response that persists at long times, and even when the instantaneous Hamiltonian is time reversal symmetric; both these features starkly contrast with equilibrium Hall currents. Interestingly, the persistent Hall effect arises from processes beyond those captured by linear response, and is a signature of the novel dynamics in out-of-equilibrium systems. We propose quenches in two-band Dirac systems as natural venues to realize persistent Hall currents, which exist when either mirror or time-reversal symmetry are broken (before or after the quench). Its long time persistence, as well as sensitivity to symmetry breaking, allow it to be used as a sensitive diagnostic of the complex out-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.

Energy dissipation is added phenomenologically by modifying Eq. (5) of the paper with a Landau-Lifshitz-Gilbert term

$$\frac{\partial\hat{\mathbf{n}}}{\partial t} = 2\mathbf d \times \hat{\mathbf{n}} \color{red}{-\gamma \hat{\mathbf{n}} \times \frac{\partial\hat{\mathbf{n}}}{\partial t}}.$$

This allows for a problem that is still analytically tractable, but for $\gamma>0$, the system relaxes to zero current. However, if $\gamma$ is small, a finite plateau is still possible.

# Experimental possibilities

The "pulse" becomes a momentum kick in cold atom experiments with two reasonable systems being prime candidates:

1. Quench of the fermionic Haldane model in cold atoms.
2. Thermal spin-orbit coupled bosons.

Even though the paper addresses fermions, #2 has all of the basic features needed to see the effect.

# Outlook

• Inclusion of a trap
• Inclusion of momentum relaxation
• Simulating the real thermal boson experiment in a trap for a potential experiment.
• Quenching 3D topological phases: What equilibrium responses survive? e.g. Time-dependent Axionic field for a 3D TI with broken time-reversal symmetry.
• Quenching strongly interacting systems with emergent topological properties (e.g. fractional quantum Hall)
• What universal features can be identified?