Directional dissipation can concentrate relaxation modes in space, but connecting this accumulation to controlled microscopic processes in correlated matter requires separating virtual charge motion from spin coherence. We study this connection in a half-filled Hubbard chain with reciprocal hopping and number-conserving, direction-selective returns of virtual doublon--hole defects. Eliminating charge defects and then Mott coherences yields asymmetric spin-exchange rates under an explicit separation of timescales, with full short-chain dynamics supporting the reduction on finite exchange times. Balanced random returns concentrate the stationary population and several low-lying right modes at sample-selected positions rather than a predetermined edge, producing random Liouvillian skin localization despite zero end-to-end logarithmic rate bias. The accumulated rate imbalance determines an exact finite-density hard-core stationary state and a one-particle activated relaxation scale governed by random barriers. This connection between locally calibrated return rates, many-body stationary weights and slow relaxation offers a means of controlling transport in constrained open quantum matter without changing the reciprocal Hamiltonian.
Liouvillian skin effects are usually associated with dissipation whose rates favor unidirectional flow. In this work, we show that directional edge localization can emerge even when population exchange between sites is exactly balanced, with a single tunable phase parameter
α deciding their direction and a dual winding structure deciding their nature. Although this number-conserving bath is known for eigenstate selection, we demonstrate here that its phase controls a steady current, which Hamiltonian hopping converts to directional edge localization. Further, we study the spectral winding structure by independently twisting the left (ket) and right (bra) vector indices of the density matrix, revealing two distinct windings whose relationship is dictated by an antiunitary mirror symmetry. Nearest-neighbor jump operators break this symmetry: both windings coincide, giving rise to a common spectral winding
W0(α)=±1, producing a unipolar skin effect in which the density accumulates at a specific edge. However, next nearest neighbor jump preserve it. The two windings are forced to be opposite, and the ket and bra are pushed to opposite edges, giving a bipolar skin effect of coherences present in eigenmodes, without edge localization of the density in the steady state. Remarkably, in a dimerized chain the phase-controlled density skin effect gives the steady-state zero modes a size-independent weight at the skin edge, accompanied by a kink at the topological transition. In addition, the relaxation time grows linearly with the system size, however at specific phases
α where the jump operators are rendered Hermitian, edge-localized eigenmodes with skin character coexist with diffusive relaxation.
The single orbital, one-dimensional, Hatano-Nelson Hamiltonian provides deep insight into the physics of non-Hermiticity, resulting from asymmetric left/right hopping, and its connections to localization. In the absence of disorder, its single particle eigenvalues
Eα lie on an ellipse in the complex plane whose extent in the imaginary direction is controlled by the degree of asymmetry. When randomness is introduced, two sets of real eigenvalues emerge at the extremes of the largest and smallest real part of
Eα. These real eigenvalues are associated with localized eigenvectors. For spinless fermions, increasing near-neighbor interactions first cause a transition to a charge density wave phase, and ultimately, on finite lattices, a collapse of all eigenvalues to the real axis. In this paper, we explore the presence of real eigenvalues in the interacting, two-particle sector for the spinful case (Hubbard model) in a two-chain (two-band) geometry with a Hermitian interchain hopping. Our key results are to obtain the ``phase" diagrams for the existence of a purely real spectrum, as a function of the interaction strength, degree of non-Hermiticity, and interchain hopping. We study the sensitivity to boundary conditions of the spectral properties of our two-chain model with winding number analysis and explore the relationship between PBC doublon states and OBC skin modes. To address the question of stability in such non-equilibrium systems, we solve the dynamics at low filling according to Lindbladian evolution and find that the non-Hermitian description is able to qualitatively describe such systems.
We study a non-Abelian Moore-Read fractional Chern insulator under a translation-preserving, nonreciprocal deformation that generates the non-Hermitian skin effect under open boundaries. The model combines the imaginary-gauge Hatano-Nelson deformation with a kagome-lattice three-body interaction designed to stabilize Moore-Read order at
ν=1/2. Our primary diagnostic is the biorthogonal
(2,4)-admissible particle-entanglement counting of the sixfold Moore-Read manifold, the standard Moore-Read fingerprint. Across three sizes (
N=16,20,24), the counting locks to the clean references 1308, 3965, and 9282 over finite nonreciprocity windows through
γ≤0.55,
0.65, and
0.74, respectively, with positive reference-rank entanglement gaps. Within every reported window the count is unchanged by the spectral readings tested; at
N=16 it is also unchanged across three reduced density operators, with all 15 combinations returning 1308. The sixfold pattern for even
Nf and the adiabatically tracked Ising-odd doublet remain separated over the tested range
γ≤0.6. Beyond a geometry-dependent threshold the instantaneous-lowest-six reference-rank gap drops sharply and its counting destabilizes. At
N=24 a sector-0 branch pair becomes complex conjugate over a narrow interval inside the delocking bracket; both continuations through the interval are delocked at the tested PES points
γ=0.76,
0.77, and
0.80. A same-lattice Abelian
ν=1/3 Laughlin realization retains its counting to
γ=1.0, so its counting is the more robust. On the torus the eigenstates remain extended; under open boundaries the right and left states skin-localize at opposite edges while the biorthogonal particle-entanglement spectrum is invariant under the imaginary-gauge similarity, so the torus and the open cylinder probe the same deformation under periodic and open boundaries.
We study the effect of repulsive interactions on skin modes and entanglement in the unidirectional Bose--Hubbard model. Although the ground state of this integrable model undergoes a superfluid--Mott transition with suppressed skin accumulation, the corresponding change in entanglement depends on the selected many-body state. We compare the ground state with the steady state, defined as the largest-imaginary-energy eigenstate in the zero-momentum sector. For sixteen sites at unit filling, we find that the ground-state density approaches uniform filling and its entanglement decreases toward the Mott limit, whereas the steady states exhibit a nonmonotonic entanglement crossover. At intermediate interaction (
U/t=10), the second Rényi entropy of the steady state develops four spatial maxima. We show that these maxima are accounted for by competing subsystem-number sectors within a dominant configuration manifold of four doublons and four holons, but not by the subsystem particle-number variance alone. The dominant global onsite-pair manifold retains the same entropy peak structure. At strong interaction, projection onto the one-doublon--one-holon manifold closely reproduces the full entropy profile and its two edge peaks. Furthermore, we demonstrate that the many-body winding about the origin remains nonzero at strong interaction; an exact two-site example shows how it becomes ill-defined in the singular projected
U/t→∞ limit. Our results distinguish ground-state skin suppression from state-selective entanglement and point-gap topology.
We revisit the fate of the skin modes in many-body non-Hermitian fermionic systems. Contrary to the single-particle case, the many-body ground state cannot exhibit an exponential localization of all eigenstates due to the Pauli exclusion principle. However, asymmetry can still exist in the density profile, which can be quantified using the imbalance between the two halves of the system. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) chain as an illustration, we show the existence of two distinct scaling regimes for the imbalance. In the first one, the imbalance grows linearly with the system size, as generically expected. In the second one, the imbalance saturates to a finite value. By combining high-precision exact diagonalization calculations and analytical arguments, we observe that the imbalance does not scale when the occupied bands can be deformed to their Hermitian limit. This suggests a direct connection between the corresponding bulk topological invariants and the skin effect in many-body systems. Importantly, this relation also holds for interacting systems.