A new family of non-Hermitian skin effects from kinetic constraints

The laws of quantum mechanics are built on the assumption that energy is conserved. Mathematically, this is encoded in the fact that the energy is represented by a Hermitian operator. In a real quantum system, however, energy leaks into the environment as quantum states decohere due to noise and dissipation. This process can be modeled by using a non-Hermitian operator that captures how energy and information are gradually lost. When such non-Hermitian systems evolve in time, they behave in ways that challenge the conventions of ordinary quantum matter.

A striking example is the non-Hermitian skin effect, in which an imbalance in the flow of charge causes nearly all particles to cluster at the boundary of a system. For the familiar particle in a box, it is as if every possible particle state is clustered around the right side of the box, rather than spread uniformly. Owing in part to a flourishing of experimental realizations, which range from photonic lattices to cold atoms, extensive theoretical effort has gone toward characterizing and classifying the skin effect. This research, however, has almost exclusively focused on systems without interactions.

In a recent paper published in Physical Review Letters, we uncovered a new family of skin effects that are irreducibly interacting—that is, they only occur when interactions between particles are strong. In fact, these interactions are so strong that they prevent individual charges from moving at all. Particles in these systems are called fractons because they are either restricted to move on fractional sub-regions of space or cannot move at all. For example, in the dipole skin effect, isolated charges are immobile fractons, but pairs of charges form mobile dipoles. We chose to focus on fractons for two reasons. First, their reduced mobility directly competes with the skin effect. While the latter tends to push charges towards a boundary, the charges themselves cannot easily move. Second, mobility restrictions make our systems intrinsically interacting, so any putative skin effect is not adiabatically connected to the conventional one.

To evade this mobility restriction, a positive and a negative charge must conspire to move together as a dipole. The interplay between this constraint and non-hermiticity makes dipoles accumulate at the edge of a system, which we dubbed the “dipole skin effect.” Other interacting skin effects arise when this principle is extended to more complex bound states of particles, like quadrupoles and octupoles. Unlike the original phenomenon, these interacting cousins cannot be detected by simply measuring the charge buildup on one edge, and thus require new experimental signatures.

Not having access to a non-interacting limit, we had to rely on more general properties of our theories, like conservation laws. In the conventional skin effect, charges can hop around, but the total charge in a system is conserved. When the hopping is asymmetric between left and right, negative charges move to one edge and positive holes remain on the opposite edge—the skin effect. This process is simply the generation of a dipole moment in the system, which we took as the key feature of the skin effect. The advantage of this new definition is that it holds regardless of interaction strength.

The dipole skin effect then has a very similar explanation. Although charges are frozen, local dipoles can hop freely. Consequently, both the total charge and the total dipole moment remain conserved. When there is an imbalance in the dipole hopping, positively oriented dipoles move to one edge, leaving opposite dipoles on the other. The result is a dipole of dipoles, i.e., a quadrupole. This pattern repeats for a hierarchy of increasingly constrained models: the signature of an m-pole skin effect is that conserved m-poles accumulate to form a (m+1)-pole moment.

By introducing a class of non-Hermitian skin effects having kinetic constraints, we extended the skin effect to the interacting regime and clarified the role of conservation laws. From an experimental point of view, our skin effects are detected by a simple observable: the m-th multipole moment of the charge distribution in a sample, which is readily measured. Lastly, we also found that these interacting skin effects dampen the spread of quantum correlations. For instance, as dipoles flow to one edge, the quadrupole moment grows large. Since there are fewer and fewer quantum states accessible with a large quadrupole moment, the system cannot be highly entangled. From this point of view, our work offers another direction to study how fast quantum systems lose their quantumness when coupled to an environment.