Majorana Scars as Group Singlets

In some quantum many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [arXiv:2007.00845] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (it is not a symmetry of the Hamiltonian). The quantum many-body scars are invariant under this group, while all other states are not. Here we apply this idea to lattice systems containing $M$ Majorana fermions per site. The Hilbert space for $N$ sites may be decomposed under the action of the O$(N)\times$O$(M)$ group, and the scars are the SO$(N)$ singlets. For any even $M$ there are two families of scars. One of them, which we call the $\eta$ states, is symmetric under the group O$(N)$. The other, the $\zeta$ states, has the SO$(N)$ invariance. For $M=4$, where our construction reduces to spin-$1/2$ fermions on a lattice with local interactions, the former family are the $N+1$ $\eta$-pairing states, while the latter are the $N+1$ states of maximum spin. We generalize this construction to $M>4$. For $M=6$ we exhibit explicit formulae for the scar states and use them to calculate the bipartite entanglement entropy analytically. For large $N$, it grows logarithmically with the sub-system size. We present a general argument that any group-invariant scars should have the entanglement entropy that is parametrically smaller than that of typical states. The energies of the scars we find are not equidistant in general but can be made so by choosing Hamiltonian parameters. For $M>6$ we find that with local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a non-local interaction term. We derive the dimension of each scar family and show the scars could have a large contribution to the density of states for small $N$.Comment: 18 pages, 1 table, 10 figures; v2: changed parameters to improve presentation, added several new results including a bound on entropy for group-invariant scar

Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks

Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spin-orbit coupling (SOC). For example, theory [1-4] indicates that the interface between a one-dimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [5-8]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality S-Sm system with uniformly transparent interfaces [9] and a hard induced gap, indicted by strongly suppressed sub gap tunneling conductance [10]. Here we report the realization of a two-dimensional (2D) InAs/InGaAs heterostructure with epitaxial Al, yielding a planar S-Sm system with structural and transport characteristics as good as the epitaxial wires. The realization of 2D epitaxial S-Sm systems represent a significant advance over wires, allowing extended networks via top-down processing. Among numerous potential applications, this new material system can serve as a platform for complex networks of topological superconductors with gate-controlled Majorana zero modes [1-4]. We demonstrate gateable Josephson junctions and a highly transparent 2D S-Sm interface based on the product of excess current and normal state resistance

Group theoretic approach to many-body scar states in fermionic lattice models

It has been shown [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that three families of highly symmetric states are many-body scars for any spin-1/2 fermionic Hamiltonian of the form H-0 + OT, where T is a generator of an appropriate Lie group. One of these families consists of the well-known eta-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine tuning. The explicit H-0 + OT decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write all the generators T that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the "revivals." A full numerical study of an extended two-dimensional tJU model explicitly illustrates the novel properties of the invariant scars and supports our findings.ISSN:2643-156