Direct coupling between gapless bosons and a Fermi surface results in the destruction of Landau quasiparticles and a breakdown of Fermi liquid theory. Such a non-Fermi liquid phase arises in spin-orbit coupled ferromagnets with spontaneously broken c
ontinuous symmetries due to strong coupling between rotational Goldstone modes and itinerant electrons. These systems provide an experimentally accessible context for studying non-Fermi liquid physics. Possible examples include low-density Rashba coupled electron gases, which have a natural tendency towards spontaneous ferromagnetism, or topological insulator surface states with proximity-induced ferromagnetism. Crucially, unlike the related case of a spontaneous nematic distortion of the Fermi surface, for which the non-Fermi liquid regime is expected to be masked by a superconducting dome, we show that the non-Fermi liquid phase in spin-orbit coupled ferromagnets is stable.
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it
has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state. Here we show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges. The time evolution of a simple, highly excited, initial state is used to reveal quantum coherent edge spins. In particular, we demonstrate, using theoretical arguments and numerical simulation, the coherent revival of an edge spin over a time scale that grows exponentially bigger with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled to a hot many body system will rapidly lose coherence.
Topological phases which host Majorana fermions can not be identified via local order parameters. We give simple nonlocal order parameters to distinguish quasi-one-dimensional (1D) topological superconductors of spinless fermions, for any interacting
model in the absence of time reversal symmetry. These string or brane order parameters are natural for measurements in cold atom systems using quantum gas microscopy. We propose them as a way to identify symmetry-protected topological phases of Majorana fermions in cold atom experiments via bulk rather than edge degrees of freedom. Subsequently, we study two-dimensional (2D) topological superconductors via the quasi-1D limit of coupling $N$ identical chains on the cylinder. We classify the symmetric, interacting topological phases protected by the additional $mathbb{Z}_N$ translation symmetry. The phases include quasi-1D analogs of (i) the $p+ip$ chiral topological superconductor, which can be distinguished up to the 2D Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise general rules for constructing nonlocal order parameters which distinguish the phases. These rules encode the signature of the fermionic topological phase in the symmetry properties of the terminating operators of the nonlocal string or brane. The nonlocal order parameters for some of these phases simply involve a product of the string order parameters for the individual chains. Finally, we give a physical picture of one of the topological phases as a condensate of certain defects, which motivates the form of the nonlocal order parameter and is reminiscent of higher dimensional constructions of topological phases.
