Dynamical Mott-Skin Effects

Updated 9 April 2026

Dynamical Mott-skin effects are defined as boundary-localized many-body excitations arising from the interplay of strong correlations, non-Hermiticity, and topology in Mott insulators and related systems.
Advanced methodologies such as DMFT, exact diagonalization, and ARPES identify these effects by quantifying spatial profiles, spectral weight redistributions, and quasiparticle renormalizations at interfaces and surfaces.
These phenomena differ from conventional skin effects by selectively localizing spin or orbital degrees of freedom while maintaining a gapped charge response in the strongly correlated bulk.

Dynamical Mott-skin effects refer to the boundary-localized response and selective penetration of correlated many-body excitations, typically within Mott insulating or strongly correlated lattice models, under conditions of spatial inhomogeneity, non-Hermiticity, or strong surface-bulk asymmetry. These phenomena emerge from the interplay of dynamical (frequency-dependent) correlations, topology, and open or inhomogeneous boundary conditions—resulting in robust edge-localized (skin) modes that are not simple single-particle skin effects, but reflect many-body correlation physics such as Mottness, quasiparticle mass renormalization, and the selective localization or delocalization of collective excitations. The "skin" manifests as a spatially exponential suppression (or enhancement) of low-energy spectral weight and coherent response in particular degrees of freedom (charge, spin, or orbital channels), with signatures in dynamics, spectral properties, and transport. Common realizations include non-Hermitian many-body systems, Mott-insulator/topological-insulator interfaces, and doped correlated surfaces.

1. Model Realizations and Definitions

Dynamical Mott-skin effects can be instantiated in a variety of microscopic settings, each tying the boundary-localized response to correlation-driven phenomena inaccessible to non-interacting models.

Non-Hermitian Bose-Hubbard Chains: In one-dimensional bosonic chains with two spin flavors and asymmetric (non-Hermitian) hopping, strong on-site and interspecies interactions ( $U, V \gg t$ ) enforce local charge constraints, yielding an effective spin-$1/2$ chain. The Mott skin effect appears as boundary-localized spin (magnon) excitations, whereas the charge sector remains uniformly gapped and insensitive to boundaries (Yoshida et al., 2023).
Interacting Fermion Models with Asymmetric Hopping: In Hubbard chains subject to strong asymmetric hopping, real-space DMFT studies reveal a crossover between traditional non-Hermitian skin effects and correlation-driven suppression of amplification. The spatial profile and degree of localization depend on the interaction strength and hopping asymmetry, defining a dynamical phase boundary (Rangi et al., 25 Jul 2025).
Heterostructures (TI/MI Interfaces): Heterostructures of topological and Mott insulators exhibit Mott-skin layers at interfaces. The TI edge penetrates the Mott insulator, inducing a boundary layer of heavy quasiparticles, the extent and metallicity of which are dynamically set by the interface tunneling and the frequency dependence of the self-energy (Ueda et al., 2013).
Surface-doped Multiorbital Mott Insulators: In systems such as alkali-dosed Ca $_2$ RuO $_4$ , ARPES reveals a single-band metallic skin at the surface. Cluster and DMFT modeling attribute this to orbital-selective hybridization creating in-gap surface metallic states, a dynamical process not captured by homogeneous doping pictures (Horio et al., 2023).
Dissipative Integrable Models: Exact solutions in dissipative Bose-Hubbard chains subject to finely tuned loss rates demonstrate the persistence of boundary-localized Mott-skin excitations even in the presence of disorder or dissipation (Ekman et al., 2024).

2. Mechanisms: Dynamical Correlations, Topology, and Non-Hermiticity

The essential feature of Mott-skin effects is their dynamical and collective nature:

Frequency-Dependent Self-Energy: The spatial variation and finite-lifetime (imaginary) parts of the self-energy, as computed self-consistently via DMFT or Bethe ansatz, are responsible for both the gapping of the bulk (Mott physics) and the emergence of edge-localized low-energy spectral weight (Yoshida, 2020, Ueda et al., 2013).
Suppression and Reemergence of Skin Modes: Strong interactions open a Mott gap, suppressing single-particle amplification and leading to exponential decay of the boundary-to-boundary Green's function (Rangi et al., 25 Jul 2025). However, sufficiently strong non-Hermiticity (e.g., large asymmetric hopping) can overcome this suppression, restoring skin-mode amplification even in the correlated regime—a key signature of a dynamical Mott-skin crossover.
Point-Gap Topology and Many-Body Winding: In non-Hermitian models, a quantized spin (or many-body) winding number under twisted boundary conditions characterizes the point-gap topology in the spectrum. This topological invariant directly predicts the emergence of skin (edge-localized) states in the spin sector, sharply contrasting with charge (which remains non-topological and delocalized in the Mott regime) (Yoshida et al., 2023).
Surface Band Renormalization and Charge Transfer: At interfaces or surfaces, modified hopping amplitudes and charge redistribution drive the surface layers closer to half-filling, enhancing the effective interactions and reducing the local quasiparticle weight, which produces a dead (skin) layer of suppressed coherence (Nourafkan et al., 2011).

Table: Mechanism—Degree of Freedom—Boundary Localization

Mechanism	Affected DoF	Skin Localization Manifestation
Point-gap (spin) topology (Yoshida et al., 2023)	Spin	Edge-accumulation of spin excitations
Heavy quasiparticles (Ueda et al., 2013)	Charge (selective)	Interfacial metal with suppressed Z
Orbital-selective hybridization (Horio et al., 2023)	Orbital	Surface metallic skin in a single band
Nonreciprocal hopping + interactions (Rangi et al., 25 Jul 2025, Zhang et al., 2020)	Charge/Spin	Crossover from skin mode to Mott-decoupled dynamics

3. Dynamical and Spectral Signatures

Dynamical Mott-skin effects are sharply visible in both static and time-dependent observables:

Boundary Sensitivity: Under open boundary conditions, skin-localized states or spectral weight manifest as pronounced differences in the local density of states or pseudo-spectrum compared to periodic boundaries (Yoshida, 2020, Yoshida et al., 2023).
Real-Time Evolution: In models with asymmetric hopping, the spin sector displays edge accumulation while the charge sector becomes uniform post-transient. The timescale for spin (magnon) pileup at the edge is $t_* \sim 1/|J_+ - J_-|$ (Yoshida et al., 2023).
Pseudo-Spectral Weight Dependence: The local pseudo-spectral weight $A_{\rm ps}(\omega)$ exhibits strong boundary-condition-dependent peaks only when a point-gap (skin) topology is present, and not in the line-gap (ordinary insulating) regime (Yoshida, 2020).
Green's Function Amplification/Decay Rates: The boundary-to-boundary Green's function $G_{1N}(\omega)$ reflects skin amplification for nonzero hopping asymmetry. Increasing interaction first suppresses (Mott screens) the amplification, but sufficiently strong asymmetry restores it, mapping a correlation-driven phase boundary (Rangi et al., 25 Jul 2025).
Surface Quasiparticle Weight Suppression: In classical Mott-skin ("dead layer") scenarios at metallic surfaces, the quasiparticle residue decays exponentially with depth; the dead layer thickness diverges near the insulator transition (Nourafkan et al., 2011).

4. Distinctions from Conventional Skin Effects

Dynamical Mott-skin effects are categorically distinct from single-particle non-Hermitian skin effects:

In non-interacting systems, skin effects arise from non-reciprocity in single-particle band structures (e.g., the Hatano–Nelson model), resulting in both charge and spin accumulation at boundaries (Yoshida et al., 2023, Rangi et al., 25 Jul 2025).
In Mott regimes, strong interactions freeze certain degrees of freedom (e.g., charge), decoupling them from boundary sensitivity. Only specific collective excitations—typically spin or orbital—exhibit nontrivial skin localization, governed by correlated topological invariants and the dynamical structure of the self-energy (Yoshida et al., 2023, Horio et al., 2023).
Dynamical Mott-skin effects can persist under finite disorder, inhomogeneous boundary conditions, or bulk-broken symmetries, provided the relevant correlation and gap conditions are satisfied (Ekman et al., 2024).

5. Methodologies for Detection and Characterization

A variety of analytic, numerical, and experimental methodologies are employed to identify and quantify dynamical Mott-skin effects:

Dynamical Mean Field Theory (DMFT and R-DMFT): Both homogeneous and inhomogeneous (layered) DMFT schemes model frequency-dependent self-energies and boundary effects, enabling calculation of quasiparticle weights, spectral functions, and real-space profiles (Yoshida, 2020, Nourafkan et al., 2011, Ueda et al., 2013, Rangi et al., 25 Jul 2025).
Cluster Models and CPT: For surface-dosed systems, cluster diagonalization with cluster perturbation theory is used to analyze in-gap spectral features and the orbital selectivity of surface skins (Horio et al., 2023).
Bethe Ansatz and Exact Integrability: In dissipative Bose-Hubbard chains tuned to critical loss rates, the Bethe ansatz yields closed-form descriptions of the spectrum, localization profiles, and phase transitions between skin, Mott, and Bose-glass regimes (Ekman et al., 2024).
Numerical Diagonalization and MPS/DMRG: Many-body ground states, excitation gaps, and time-evolving wavefunctions are obtained via exact diagonalization and non-Hermitian matrix-product-state methods, capturing the interplay of interactions and non-Hermiticity (Zhang et al., 2020).
Experimental Probes: Angular-resolved photoemission (ARPES), scanning tunneling microscopy (STM), and time-resolved pump-probe optics directly image spectral-weight redistribution and the emergence of skin metallic states. In cold-atom systems, quantum-gas microscopy and time-of-flight measurements reveal boundary profiles and dynamical expansion velocities (Horio et al., 2023, Ekman et al., 2024, Zhang et al., 2020).

6. Experimental Realizations and Prospects

Experimental implementation and detection of dynamical Mott-skin effects have advanced through several platforms:

Layered and Interface Systems: Fabricated heterostructures (TI/MI interfaces) and atomically resolved surfaces have demonstrated Mott-skin signatures via both transport and spectroscopy (Ueda et al., 2013, Nourafkan et al., 2011).
Alkali-metal Dosing: Surface-doping of Mott insulators, notably Ca $_2$ RuO $_4$ , achieves selective orbital hybridization and skin metallicity, with direct ARPES imaging (Horio et al., 2023).
Cold Atom Lattices: One-dimensional optical lattices with engineered non-reciprocal hopping (via Floquet modulation, local loss, or synthetic gauge fields) provide tunable settings to observe dynamical skin effects, measurable via in situ density and correlation profiles (Ekman et al., 2024, Zhang et al., 2020, Rangi et al., 25 Jul 2025).
Photonic and Circuit-QED Lattices: Nonlinear photonic arrays and circuit-QED systems with designer dissipation and interactions represent alternative routes due to their inherent control and accessibility to time-resolved observables (Yoshida et al., 2023).

A plausible implication is that further exploration of higher-dimensional correlated skin effects, multi-orbital selectivity, and time-dependent control (e.g., via dynamic drive of hybridization or dissipation) will expand the taxonomy of Mott-skin phenomena and their applications in quantum simulation and topological matter engineering.

7. Outlook and Theoretical Implications

Dynamical Mott-skin effects unify non-Hermitian topology, correlation physics, and boundary dynamics in a new framework:

Correlation–Topology Interplay: The presence or absence of skin phenomena is dynamically controlled by the competition between non-Hermitian band topology and strong correlations, reflected in frequency-dependent self-energies and many-body winding invariants (Yoshida et al., 2023, Yoshida, 2020).
Non-trivial Phase Diagrams: Many-body systems in the $(U, \gamma)$ or $1/2$0 plane exhibit sharp phase boundaries between skin-dominated, correlation-dominated (Mott), and mixed regimes. Transitions can be mapped by observables such as amplification rates, excitation gaps, or spectral-weight shifts (Rangi et al., 25 Jul 2025, Ekman et al., 2024).
Surface/Edge Quantum Engineering: Dynamical Mott-skin effects suggest avenues for engineering robust, tunable, edge-localized metallic or magnetic responses in correlated materials, with potential device applications based on selective boundary control.
Exceptional Points and Disorder Effects: The persistence of Mott-skin localization through disorder and at exceptional degeneracy points in the spectrum connects these phenomena to broader concepts in non-Hermitian physics and quantum criticality (Ekman et al., 2024).

Continued theoretical and experimental work is expected to clarify the universal features, anomalies, and control mechanisms underlying dynamical Mott-skin phenomena in strongly interacting systems, deepening understanding of open quantum matter at the intersection of topology, correlations, and non-equilibrium dynamics.