arXiv subjects

Pedro Fittipaldi de Castro

Publications and source records attributed to Pedro Fittipaldi de Castro.

5 recordsLinked to original sources

arXiv2026

Thermalization hierarchy from irreducible degrees of freedom

The decomposition of the Hilbert space of a quantum many-body system into the irreducible representations of its bond and commutant algebras yields a finer structure of dynamically isolated subspaces than the mere decomposition into symmetry sectors. While it has been recognized that subspaces associated with low bond-irrep dimensions $D_λ$ tend to violate the eigenstate thermalization hypothesis (ETH), here we show that $D_λ$ controls thermalization continuously across the full spectrum of dynamical subspaces. Using SU(2)-symmetric spin-1/2 chains as a paradigmatic example, we demonstrate that $\mathrm{log} \ D_λ$ quantitatively accounts for the average eigenstate entanglement entropy within each sector, establishing a thermalization hierarchy that interpolates from exact quantum many-body scars at $D_λ=1$ to volume-law ergodic states at large $D_λ$. To make this concrete, we introduce the notion of irreducible degrees of freedom (IDOF), defined as the number of independently-varying spatial coordinates parametrizing a many-body state within a given bond-algebra sector, which provides a microscopic interpretation of $D_λ$ and of the resulting thermalization hierarchy. Finally, we show that by selectively breaking symmetries while preserving chosen bond-algebra sectors, one can embed families of nonthermal eigenstates at prescribed entanglement levels into an otherwise ergodic spectrum, generalizing restricted spectrum-generating algebras from towers of individual states to entire dynamical subspaces.

quant-ph↗

arXiv2026

Complex Wannier centers and drifting Wannier functions in non-Hermitian Hamiltonians

The extension of topological band theory to non-Hermitian Hamiltonians with line energy gaps remains largely unexplored, despite early indications of rich underlying physics. In these systems, Wilson loops, the objects characterizing polarization, become nonunitary. Yet, the physical consequences of this nonunitarity have remained unclear. Using biorthonormal quantum mechanics, we introduce the concept of complex Wannier centers, defined from the gauge-invariant eigenvalues of nonunitary Wilson loops. Complex Wannier centers acquire physical meaning through the breaking of reciprocity in their associated Wannier functions. When the centroid of a Wannier function shifts into the complex plane, it acquires an effective momentum offset that produces directional drift over time. We analyze how symmetries constrain complex Wannier centers and identify symmetry-protected Wannier configurations in pseudo-Hermitian Hamiltonians, where the centers are either real or form complex-conjugate pairs, as determined by conserved "Krein signatures" of the projected metric operator of pseudo-Hermiticity. We further show that the Krein structure of the Wilson loop can establish a bulk-boundary correspondence: in a system with anticommuting pseudo-Hermitian metric and (pseudo) inversion symmetries, the behavior of complex Wannier centers predicts the existence of a filling anomaly in the occupied bands and whether the resulting edge modes experience gain or loss. Finally, we propose an implementation of this system that enables experimental tests of our predictions.

cond-mat.mes-hall↗

arXiv2025

A dynamical order parameter for the transition to nonergodic dynamics in the discrete nonlinear Schrödinger equation

The discrete nonlinear Schrödinger equation (DNLSE) exhibits a transition from ergodic, delocalized dynamics to a weakly nonergodic regime characterized by breather formation; yet, a precise characterization of this transition has remained elusive. By sampling many microcanonically equivalent initial conditions, we identify the asymptotic ensemble variance of the Kolmogorov-Sinai entropy as a dynamical order parameter that vanishes in the ergodic phase and becomes finite once ergodicity is broken. The relaxation time governing the ensemble convergence of the KS entropy displays an essential singularity at the transition, yielding a sharp boundary between the two dynamical regimes. This framework provides a trajectory-independent method for detecting ergodicity breaking that is broadly applicable to nonlinear lattice systems with conserved quantities.

cond-mat.stat-mech↗

arXiv2025

Solitons with Self-induced Topological Nonreciprocity

The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation. This nonreciprocal behavior, dependent on soliton power, arises from the interplay between linear and nonlinear terms in the equations of motion. Initially stable at high power, solitons exhibit nonreciprocal instabilities as power decreases, leading to unidirectional acceleration and amplification. This behavior is topologically protected by winding numbers on the solitons' mean-field Hamiltonian and their stability matrix, linking nonlinear dynamics and point gap topology in non-Hermitian Hamiltonians.

nlin.PS↗

arXiv2024

Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice

The non-Hermitian skin effect (NHSE) is a distinctive topological phenomenon observed in nonHermitian systems. Recently, there has been considerable interest in exploring higher-order NHSE occurrences in two and three dimensions. In such systems, topological edge states collapse into a corner while bulk states remain delocalized. Through a Hermitian-non-Hermitian correspondence, this study predicts and experimentally observes the higher-order NHSE in an acoustic Kagome lattice possessing nonreciprocal hoppings. By rotating the frequency spectrum and employing complexfrequency excitation techniques, we observe the localization of acoustic energy towards a corner of the lattice in the topologically nontrivial phase, even when the source is located far from that corner. In contrast, the acoustic energy spreads out when excited at the frequencies hosting the bulk states. These observations are unequivocal evidence of the higher-order NHSE.

cond-mat.mes-hall↗