arXiv subjects

Wladimir A. Benalcazar

Publications and source records attributed to Wladimir A. Benalcazar.

At least 19 recordsLinked to original sources

arXiv2026

A Spatial Localizer for Constituent-Resolved Exciton Wannier Functions

Excitons are composite quasiparticles: beyond a center-of-mass position, each carries an internal electron-hole dipole governing its coupling to electric fields and other excitons. Exciton Wannier functions locally represent exciton bands, but resolving this dipole requires localizing the electron and hole simultaneously. We show that, in one dimension, the projected electron and hole position operators fail to commute when the covariant derivative of the quantum geometric dipole (QGD) matrix (the difference between the hole and electron non-Abelian Berry connections) is nonzero. This precludes a common eigenbasis and bounds the joint electron-hole spread from below. For one band, the internal dipole is gauge invariant and center-of-mass methods suffice; for multiple bands, no existing construction yields a gauge minimizing both position uncertainties. We introduce an ``exciton spatial localizer,'' a Hermitian operator embedding both projected positions in a Clifford-algebra structure. Its spectral minima locate the exciton's center-of-mass and dipole coordinates, while its eigenvectors yield exciton Wannier functions jointly localized in electron and hole coordinates without gauge fixing, an ansatz, or iterative optimization. In an interacting bilayer model, combined reflection--time-reversal symmetry or a nonsymmorphic particle--hole symmetry forces the QGD matrix to be traceless at every momentum while allowing it to remain nonzero. A two-band exciton subspace with zero net internal dipole then decomposes into a symmetry-related pair of exciton Wannier functions with opposite center-of-mass positions and internal dipoles. Adding the interlayer dipole as a Clifford component further separates intralayer and interlayer exciton Wannier functions in a six-band subspace.

cond-mat.mtrl-sci↗

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↗

arXiv2026

A Spatial Localizer for Electrons in Insulators

The location of electrons governs phenomena ranging from chemical bonding and electric polarization to the topological classification of band insulators and the emergence of correlated states in quantum matter. While a prescription exists for finding local state representations of electrons in one-dimensional insulators, no comparably general theory exists in higher dimensions. Here, we introduce a general framework for finding the location of electrons in insulators in two and three dimensions based on the spectral properties of quantum-mechanical operators that we term Spatial Localizers. This framework naturally extends the notion of Wannier centers to insulators with boundaries, defects, and disorder, which we use to establish a position-space formulation of the bulk-defect correspondence for electronic charge. This framework also yields maximally localized electronic states. As two representative examples, we show that these states reduce to maximally localized Wannier functions in atomic insulators, whereas in Chern insulators they form coherent states that mirror the coherent-state structure of Landau levels in the quantum Hall effect.

cond-mat.mtrl-sci↗

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

Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry

In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya no-go theorem at their one-dimensional boundaries. This allows the realization of topologically-protected one-dimensional edges with nonreciprocal dynamics. However, unlike the edge states of Chern insulators, the nonreciprocal edges of HOSE phases exist only at certain edges of the two-dimensional lattice, not all, leading to corner-localized states. In this paper, we investigate the topological connections between these two systems and uncover novel non-Hermitian topological phases possessing higher-order topological knots (HOTKs). These phases arise from multiband topology protected by crystalline symmetries and host nonreciprocal edge states that circulate the entire boundary of the two-dimensional lattice. We show that phase transitions typically separate HOTK phases from complex Chern insulator phases - non-Hermitian lattices with nonzero Chern numbers protected by imaginary line gaps in the presence of time-reversal symmetry.

cond-mat.mes-hall↗

arXiv2025

Nonlinear breathers with crystalline symmetries

Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and exponentially localized Wannier states are a central tool in the classification of band structures with crystalline symmetries. Moreover, the quantized transport observed in nonlinear Thouless pumps relies on the fact that -- at least in a specific model -- discrete breathers recover Wannier states in the limit of vanishing nonlinearity. Motivated by these observations, we investigate the correspondence between nonlinear breathers and exponentially localised Wannier states for a family of discrete nonlinear Schrödinger equations with crystalline symmetries. We develop a formalism to analytically predict the breathers' spectrum, center of mass and symmetry data, and apply this to nonlinear generalizations of the Su-Schrieffer-Heeger chain and the breathing kagome lattice.

cond-mat.mes-hall↗

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↗

arXiv2023

A mono-atomic orbital-based 1D topological crystalline insulator

Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk to robust observables on the edges, e.g., the existence of robust edge modes or fractional charge. In one dimension, TCIs protected by reflection symmetry have been realized in a variety of systems where each unit cell has spatially distributed degrees of freedom (SDoF). However, these realizations of TCIs face practical challenges stemming from the sensitivity of the resulting edge modes to variations in edge termination and to the local breaking of the protective spatial symmetries by inhomogeneity. Here we demonstrate topologically protected edge states in a mono-atomic, orbital-based TCI that mitigates both of these issues. By collapsing all SDoF within the unit cell to a singular point in space, we eliminate the ambiguity in unit cell definition and hence remove a prominent source of boundary termination variability. The topological observables are also more tolerant to disorder in the orbital energies. To validate this concept, we experimentally realize a lattice of mechanical resonators where each resonator acts as an "atom" that harbors two key orbital degrees of freedom having opposite reflection parity. Our measurements of this system provide direct visualization of the $sp$-hybridization between orbital modes that leads to a non-trivial band inversion in the bulk. Furthermore, as the spatial width of the resonators is tuned, one can drive a transition between a topological and trivial phase. In the future we expect our approach can be extended to realize orbital-based obstructed atomic insulators and TCIs in higher dimensions.

cond-mat.mes-hall↗

arXiv2023

Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal

Higher-order topological band theory has transformed the landscape of topological phases in quantum and classical systems. Here, we experimentally demonstrate a two-dimensional (2D) higher-order topological phase (HOTP), referred to as the multiple chiral topological phase (MCTP), which is protected by a multipole chiral number (MCN). Our realization differs from previous HOTPs in that it possesses a larger-than-unity MCN, which arises when the nearest-neighbor couplings (NNCs) are weaker than long-range couplings (LRCs). Our phase has an MCN of 4, protecting the existence of 4 mid-gap topological corner modes (TCMs) at each corner. The multiple TCMs demonstrated here could lead to enhanced quantum-inspired devices for sensing and computing. Our study also highlights the rich and untapped potential of LRC manipulation for future research in topological phases.

cond-mat.mes-hall↗

arXiv2023

Response to polarization and weak topology in Chern insulators

Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to "weak" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a "bulk-boundary correspondence", regardless of whether a Wannier representation is possible.

cond-mat.mes-hall↗

arXiv2023

Topological Phases of Photonic Crystals under Crystalline Symmetries

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one- and two dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.

cond-mat.mes-hall↗

arXiv2022

Higher-order topological pumping and its observation in photonic lattices

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. These cycles are associated with higher-order topology and can be diagnosed by their ability to produce corner-to-corner transport in certain metamaterial platforms. We experimentally verify the corner to corner transport associated with this topological pump by using an array of photonic waveguides adiabatically modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal dimensions to three spatial dimensions, our observations are equivalent to the observation of chiral hinge states in a three-dimensional second-order topological insulator.

cond-mat.mes-hall↗

arXiv2022

Photonic quadrupole topological insulator using orbital-induced synthetic flux

The rich physical properties of multiatomic molecules and crystalline structures are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. This orbital degree of freedom has also been used effectively to introduce structural diversity in a few synthetic materials including polariton lattices nonlinear photonic lattices and ultracold atoms in optical lattices. In particular, the mixing of orbitals with distinct parity representations, such as $s$ and $p$ orbitals, has been shown to be especially useful for generating systems that require alternating phase patterns, as with the sign of couplings within a lattice. Here we show that by further breaking the symmetries of such mixed-orbital lattices, it is possible to generate synthetic magnetic flux threading the lattice. This capability allows the generation of multipole higher-order topological phases in synthetic bosonic platforms, in which $π$ flux threading each plaquette of the lattice is required, and which to date have only been implemented using tailored connectivity patterns. We use this insight to experimentally demonstrate a quadrupole photonic topological insulator in a two-dimensional lattice of waveguides that leverage modes with both $s$ and $p$ orbital-type representations. We confirm the nontrivial quadrupole topology of the system by observing the presence of protected zero-dimensional states, which are spatially confined to the corners, and by confirming that these states sit at the band gap. Our approach is also applicable to a broader range of time-reversal-invariant synthetic materials that do not allow for tailored connectivity, e.g. with nanoscale geometries, and in which synthetic fluxes are essential.

physics.optics↗

arXiv2022

Chiral-Symmetric Higher-Order Topological Phases of Matter

We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers", bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.

cond-mat.str-el↗

arXiv2022

Observation of bound states in the continuum embedded in symmetry bandgaps

In the last decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg-diffraction limit, which fundamentally restricts their use to single-frequency applications. By 3D-micro printing a photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a three-dimensional photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. Moreover, we experimentally verify that just a single layer of this photonic crystal environment is sufficient. This concept significantly expands the design freedom available for developing next-generation devices with high-Q states.

physics.optics↗

arXiv2021

Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice

Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DoS) in classical wave systems. While these fractional DoS have associated states localized to the disclination's core, such states are not protected from deconfinement due to the breaking of chiral symmetry, generally leading to resonances which, even in principle, have finite lifetimes and suboptimal confinement. Here, we devise and experimentally validate in acoustic lattices a paradigm by which topological states bind to disclinations without a fractional DoS but which preserve chiral symmetry. The preservation of chiral symmetry pins the states at the mid-gap, resulting in their protected maximal confinement. The integer DoS at the defect results in two-fold degenerate states that, due to symmetry constraints, do not gap out. Our study provides a fresh perspective on the interplay between symmetry-protection in topological phases and topological defects, with possible applications in classical and quantum systems alike.

cond-mat.mes-hall↗

arXiv2021

Topological phases of the dimerized Hofstadter butterfly

In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter spectrum at certain fractional fillings, giving rise to various topological phases. In particular, we show that at $\frac{1}{2}$-filling the topological quadrupole insulator phase with a quadrupole moment quantized to $\frac{e}{2}$ and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At $\frac{1}{4}$ filling, the system can host obstructed atomic limit phases or Chern insulator phases. For those configurations gapped at fillings below $\frac{1}{4}$, the system is in Chern insulator phases of various non-vanishing Chern numbers. Across the phase diagram, both bulk-obstructed and boundary-obstructed topological phase transitions exist in this model.

cond-mat.mes-hall↗