Abstract We investigate distinct non-Hermitian skin effects (NHSEs) in real and Fock spaces induced by the interplay between the Hilbert space fragmentation and multiple non-Hermitian pumping channels. Using an extended Hatano–Nelson model with next-nearest neighbor hopping and strong interaction as an example, we found that two fermions loaded in the lattice exhibit different real-space NHSE depending on the Hilbert space fragments to which they belong. Moreover, in the high-energy sector resulting from fragmentation, the two-particle-bound states form a one-dimensional lattice in Fock space, producing a Fock-space NHSE. At half-filling, richer patterns of Fock-space skin-like localization emerge for the different fragmented energy sectors and subsectors while real-space NHSE is suppressed by many-body effects. This study extends our understanding of the interplay between NHSE and Hilbert space fragmentation and provides detailed insights into their manifestation in interacting non-Hermitian systems.
A novel analysis of finite-dimensional Hilbert space is outlined. The approach bypasses the general, inherent, difficulties present in handling angular variables in finite-dimensional problems: the finite-dimensional, d , odd prime, Hilbert space operators are underpinned with a finite geometry which provides intuitive perspectives to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite-dimensional quantum-mechanics studies. Interrelations among the Hilbert space operators revealed via their (finite) dual affine plane geometry (DAPG) underpinning are displayed and utilized in formulating the finite-dimensional ubiquitous Radon transformation and its inverse illustrating phase-space-like physics encoded in lines and points of the geometry. The finite geometry required for our study is outlined.
The reduced
k-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of
k-body observables. A proper understanding of this projection is therefore intimately related to the representability problem, a long-standing open problem in computational quantum chemistry. Given an orthonormal basis in the finite-dimensional one-particle Hilbert space, we explicitly construct an orthonormal basis of the space of Fock space operators which restricts to an orthonormal basis of the space of
k-body operators for all
k.