Degenerate States Research Articles

Stabilizer code model with noninvertible symmetries: Strange fractons, confinement, and noncommutative and non-Abelian fusion rules

We introduce a stabilizer code model with a qutrit at every edge on a square lattice and with noninvertible plaquette operators. The degeneracy of the ground state is topological as in the toric code, and it also has the usual deconfined excitations consisting of pairs of electric and magnetic charges. However, there are novel types of confined fractonic excitations composed of a cluster of adjacent faces with vanishing flux. They manifest confinement, and even larger configurations of these fractons are fully immobile although they acquire emergent internal degrees of freedom. Deconfined excitations change their nature in presence of these fractonic defects. As for instance, fractonic defects can absorb magnetic charges making magnetic monopoles exist while electric charges acquire restricted mobility. Furthermore, some generalized symmetries can annihilate any ground state and also the full sector of fully mobile excitations. All these properties can be captured via a novel type of and fusion category in which the product is associative but does not commute, and can be expressed as a sum of (operator) equivalence classes. Generalized noninvertible symmetries give rise to the feature that the fusion products form a nonunital category without a proper identity. We show that a variant of this model features a deconfined fracton liquid phase and a phase where the dual (magnetic) strings have condensed. Published by the American Physical Society 2024

Controllable switching based on vortex–antivortex pairs in exciton–polariton condensates

Abstract Vortex–antivortex pairs hold significant prospect for applications in high-capacity optical communications, multiparticle manipulations, and data processing systems. In this work, based on vortex–antivortex pairs, we explore a straightforward method to produce a 1–4 optical switch in a polariton condensate with a C-shaped potential. The switch, seeded by a degenerate state containing two vortex–antivortex pairs, can selectively target four objective states: two orthogonal states with a single vortex–antivortex pair and two concentric vortices with opposite circulations. All these topological states are stable states with the application of a single incoherent pump, while the switch is activated by an additional coherent control pulse.

Helical-photon-dressed states determining unidirectional π-electron rotations in aromatic ring molecules.

We theoretically demonstrated that helical-photon-dressed states determine the rotational directions of the π-electrons of aromatic ring molecules formed by a circularly polarized or an elliptically polarized laser. This theory was verified using a minimal three-electronic-state model under the frozen nuclei condition. The model consists of the ground state and either a doubly degenerate electronic excited state or two quasi-degenerate excited states. Three helical-photon-dressed states were derived by solving the time-dependent Schrödinger equation within the semi-classical treatment of light-molecule interactions and rotating wave approximation. The angular momenta of the two helical-photon-dressed states represent the classical rotational direction, and that of the remaining state represents the opposite rotation, that is, non-classical rotation. Classical rotation means that π-electrons have the same rotational direction as that of a given helical electric field vector and obeys the classical equations of motion. Non-classical rotation indicates that the rotational direction is opposite to that of the helical electric field vector. Non-classical rotation is forbidden in an aromatic ring molecule with high symmetry formed by a circularly polarized laser but is allowed in a low symmetric aromatic ring molecule. The sum of the angular momenta of the three dressed states is zero. This is called the sum law for the angular momentum components in this paper. Benzene (D6h) and toluene (CS) were adopted as typical aromatic ring molecules of high and low symmetries, respectively. Finally, considering the effects of nuclear vibrations in the adiabatic approximation, an expression for the π-electron angular momentum was derived and applied to toluene.

Multiring polygon super-geometric beam generation based on quasi-frequency- degeneracy state of multiaxial super- geometric mode laser

Multiring polygon super-geometric beam generation based on quasi-frequency- degeneracy state of multiaxial super- geometric mode laser

Ferromagnetic ferroelectricity due to the Kugel-Khomskii mechanism of orbital ordering assisted by atomic Hund's second rule effects

The exchange interactions in insulators depend on the orbital state of magnetic ions, obeying certain phenomenological principles, known as Goodenough-Kanamori-Anderson rules. Particularly, the ferro order of alike orbitals tends to stabilize antiferromagnetic interactions, while the antiferro order of unlike orbitals favors ferromagnetic interactions. The Kugel-Khomskii theory provides a universal view on such coupling between spin and orbital degrees of freedom, based on the superexchange processes: namely, for a given magnetic order, the occupied orbitals tend to arrange in a way to further minimize the exchange energy. Then, if two magnetic sites are connected by the spatial inversion, the antiferro orbital order should lead to the ferromagnetic coupling break the inversion symmetry. This constitutes the basic idea of our work, which provides a pathway for designing ferromagnetic ferroelectrics: the rare but fundamentally and practically important multiferroic materials. After illustrating the basic idea on toy-model examples, we propose that such behavior can be indeed realized in the van der Waals ferromagnet VI3, employing for this analysis the realistic model derived from first-principles calculations for magnetic 3d bands. We argue that the intra-atomic interactions responsible for Hund's second rule, acting against the crystal field, tend to restore the orbital degeneracy of the ionic d2 state in VI3 and, thus, provide a necessary flexibility for activating the Kugel-Khomskii mechanism of the orbital ordering. In the honeycomb lattice, this orbital ordering breaks the inversion symmetry, stabilizing the ferromagnetic-ferroelectric ground state. The symmetry breaking leads to the canting of magnetization, which can be further controlled by the magnetic field, producing a huge change of electric polarization. Published by the American Physical Society 2024

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. I. Wavefunction-based methods.

In this paper, we investigate the role of electron correlation in predicting the S1-S0 and T1-S0 excitation energies and, hence, the singlet-triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules.

Magnetic Excitations in Ferromagnetically Coupled Spin-1 Nanographenes.

In the pursuit of high-spin building blocks for the formation of covalently bonded 1D or 2D materials with controlled magnetic interactions, -electron magnetism offers an ideal framework to engineer ferromagnetic interactions between nanographenes. As a first step in this direction, we explore the spin properties of ferromagnetically coupled triangulenes-triangular nanographenes with spin . By combining in-solution synthesis of rationally designed molecular precursors with on-surface synthesis, we successfully achieve covalently bonded triangulene dimers and trimers on Au(111). Starting with the triangulene dimer, we meticulously characterize its low-energy magnetic excitations using inelastic electron tunneling spectroscopy (IETS). IETS reveals conductance steps corresponding to a quintet-to-triplet excitation, and a zero-bias peak resulting from higher-order spin-spin scattering of the five-fold degenerate ferromagnetic ground state. The Heisenberg model captures the key parameters of inter-triangulene ferromagnetic exchange, and its successful extension to the larger system validates the model's accuracy. We anticipate that incorporating ferromagnetically coupled building blocks into the repertoire of magnetic nanographenes will unlock new possibilities for designing carbon nanomaterials with complex magnetic ground states.

Floquet prethermal order by disorder

Frustrated magnets can have accidental ground state degeneracies which may be lifted by various forms of disorder, for example in the form of thermal or quantum fluctuations. This order by disorder (ObD) paradigm is well established in equilibrium and here is generalized to Floquet many-body systems. Investigating a periodically driven XXZ-compass model on the square lattice, we show that in a prethermal regime, dynamical fluctuations induced by high-frequency drives select a discrete set of states out of a degenerate ground state manifold of the lowest order Floquet Hamiltonian chosen as initial states. Remarkably, prior to the ObD selection, an unusual fluctuating regime emerges leading to a prethermalization timescale scaling linearly with the drive frequency. We argue that prethermal ObD with its unusual approach to the selected states is a generic phenomenon of driven frustrated systems and confirm it in the paradigmatic J1−J2 XX model. Published by the American Physical Society 2024

Optical properties of a hollow cylindrical quantum wire in a parallel applied magnetic field

In this theoretical study, we investigate optical properties of a hollow cylindrical quantum wire in the presence of a homogeneous magnetic field. The magnetic field is applied parallel to the axis of the quantum wire. The investigations were achieved by solving the Schrödinger equation within the effective mass approximation. The optical properties studied were absorption coefficient (AC) of electromagnetic radiation and changes in refractive index (CRI) of the hollow cylinder. The parallel applied magnetic field lifts the degeneracy of states of opposite angular momentum (the ±|m|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm |m |$$\\end{document} states, m being the angular momentum quantum number) known as the Zeeman splitting. As such, in the presence of magnetic field, AC splits into two branches, one corresponding to a transition involving the positive m states and the other corresponding to a transition involving the negative m states. Increase in intensity of the electromagnetic radiation reduces the magnitude of the AC. Presence of inner radius of the hollow cylindrical wire lowers transition energies. Apart from absorption due to the (m=0→±1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m=0 \\rightarrow \\pm 1)$$\\end{document} transitions, the presence of the inner radius also facilitates absorption due the (m=-1→0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m=-1\\rightarrow 0)$$\\end{document} transition as the magnetic field strength increases, a phenomenon that does not happen in solid cylindrical quantum wires. The presence of the inner radius also enhances AC in strong magnetic field. Increase in intensity of the electromagnetic radiation affects the CRI (here considered up to third order), introducing a normal dispersion region in an otherwise anomalous region. The parallel magnetic field also splits the CRI depending on the sign of the m states involved in the transitions.

Fluorescence Modulation through the Inverted Energy Gap Law in Triply N─B←N‐Containing Windmill‐Shaped Triazines

A series of windmill‐shape heterocyclic molecules containing three N─B←N units, TBN and its derivatives, with quasi‐planar C3 symmetric backbone, are synthesized. The parent TBN exhibits a strongly allowed, doubly degenerate lowest excited state but suffers from very low fluorescence, due to very fast nonradiative decay rate through a conical intersection (CI) as revealed by femtosecond transient absorption spectroscopy and quantum‐chemical calculations. Introducing peripheral phenyl‐ or thienyl‐groups (Ph‐TBN or Th‐TBN) induces pronounced bathochromic shifts and enhances fluorescence, which is beneficial from inhibited nonradiative pathway by the increased energy barriers to access the CI at excited state. The understanding of this rather uncommon behaviour may open routes for the design of novel fluorescence materials.

Fluorescence Modulation through the Inverted Energy Gap Law in Triply N─B←N-Containing Windmill-Shaped Triazines.

A series of windmill-shape heterocyclic molecules containing three N─B←N units, TBN and its derivatives, with quasi-planar C3 symmetric backbone, are synthesized. The parent TBN exhibits a strongly allowed, doubly degenerate lowest excited state but suffers from very low fluorescence, due to very fast nonradiative decay rate through a conical intersection (CI) as revealed by femtosecond transient absorption spectroscopy and quantum-chemical calculations. Introducing peripheral phenyl- or thienyl-groups (Ph-TBN or Th-TBN) induces pronounced bathochromic shifts and enhances fluorescence, which is beneficial from inhibited nonradiative pathway by the increased energy barriers to access the CI at excited state. The understanding of this rather uncommon behaviour may open routes for the design of novel fluorescence materials.

Mechanisms of separation of the elastic step and the thermal step

The elastic interaction causes a two‐step conversion from the low‐spin (LS) to the high‐spin state (HS) following a femtosecond laser pulse excitation. These steps occur on different timescales: a spin conversion (elastic step) in a short time due to pressure propagation and a late spin conversion (thermal step) resulting from heat diffusion. In this paper, we provide a brief review of models for spin crossover phenomena, emphasizing the role of the difference of degeneracy of the HS state and LS state and elastic interaction due to changes in local structures. We also review theoretical approaches to these effects. Additionally, to analyze the dynamical process of spin conversion after photo‐irradiation, it is necessary to consider mechanisms of heat transfer among spins. Recently, we proposed a two‐temperature model that incorporates both lattice and spin temperatures, which enables us to reproduce the two steps under an early uniformization of the lattice temperature, highlighting the importance of the timescales of these processes. Furthermore, we explore possible mechanisms to separate the two steps by examining the different timescales of processes of spin conversions by mechanical and entropic forces, and also by considering changes of local temperature due to spin conversion.

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains.

Unlocking the potential of topological order in many-body spin systems has been a key goal in quantum materials research. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg chains by covalently linking Clar's goblets-nanographenes each hosting two antiferromagnetically coupled spins. Using scanning tunnelling microscopy, we exert atomic-scale control over chain lengths, parities and exchange-coupling terminations, and probe their magnetic response via inelastic tunnelling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons. Their dispersion relation is extracted from the spatial variation of tunnelling spectral amplitudes. Depending on the parity and termination of chains, we observe varying numbers of in-gap spin-1/2 edge excitations, reflecting the degeneracy of distinct topological ground states in the thermodynamic limit. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our findings present a phase-controlled many-body platform, opening avenues toward spin-based quantum devices.

Solvation modeling and optical properties of CdSO4-Doped L-Valine crystals

The utilization of computational solvation models for crystals proves effective in determining the amalgamation of molecular structures within the crystal medium, offering valuable insights into optimized crystal properties. This study focuses on identifying the arrangement of molecular strips within the crystal, crucial for recognizing active planes and the presence of non-linear optical (NLO) properties. To delve into the crystal's intricacies, a computational model was developed, and conformational analysis was conducted to ensure NLO property. The synthesis of the CdSO4-doped L-Valine metallo-organic complex crystal was achieved through the melt-freezing technique. The computational model was constructed to elucidate the formation of sub-planes within a confirmed orthorhombic crystal lattice. Mapping the molecular charge distribution with the dispersion of charge gradient facilitated the identification of chemical potential inhibition and its equipotential nodal domains. The estimation of electron density potential over critical points of the core carbons provided further insights. Chemical dynamics on the electron content of molecules for NLO properties were investigated by screening control parameters. The inelastic scattering ability of heteronuclear bonds for enhancing boosting potential was observed. Interactive frontier orbitals of degenerate energy states were illustrated, and the chemical potential of molecular zones was analyzed in-depth.

UMRSF-TDDFT: Unrestricted Mixed-Reference Spin-Flip-TDDFT.

An unrestricted version of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (UMRSF-TDDFT) was developed based on unrestricted Kohn-Sham orbitals (UKS) with a new molecular orbital (MO) reordering scheme. Additionally, a simple yet accurate method for estimating ⟨S2⟩ expectation values was devised. UMRSF-TDDFT was benchmarked against cases where DFT, TDDFT, and SF-TDDFT traditionally fail to provide accurate descriptions. In an application to the ground and excited states of a Be atom, UMRSF-TDDFT successfully recovers the degenerate states, with its energies slightly reduced compared to its RO counterpart, due to the additional variational flexibility of UKS. A clear difference between UMRSF and U-SF-TDDFT is evident in the bond breaking of the hydrogen fluoride system, as the latter misses an important configuration. In the case of the Jahn-Teller distortion of trimethylenemethane (TMM), the relative singlet energy compared to the triplet is lower by 0.1 and 0.2 eV for UMRSF and U-SF-TDDFT, respectively, than that of MRSF-TDDFT. The reduction in UMRSF energy is attributed to spatial orbital relaxations, whereas the reduction in U-SF-TDDFT energy results from spin contamination. Overall, the additional orbital relaxations afforded by unrestricted Kohn-Sham (UKS) orbitals in UMRSF-TDDFT lead to lower total system energies compared to their restricted open-shell counterparts. This enhancement adds a practical and accurate quantum chemical theory to the existing RO variant for addressing challenging systems where traditional quantum theories suffer.

Domain Dynamics Response to Polarization Switching in Relaxor Ferroelectrics.

Nanoscale polar regions, or nanodomains (NDs), are crucial for understanding the domain structure and high susceptibility of relaxors. However, unveiling the evolution and function of NDs during polarization switching at the microscopic level is of great challenge. The experimental in situ characterization of NDs under electric-field perturbations, and computational accurate prediction of the dipole switching within a sufficiently large supercell, are notoriously tricky and tedious. These difficulties hinder a full understanding of the link between micro domain dynamics and macro polarization switching. Herein, the real-time evolution of NDs at the nanoscale is observed and visualized during polarization switching in an exemplary relaxor system of Bi5- xLaxMg0.5Ti3.5O15. Two fundamentally different domain switching pathways and dynamic characteristics are revealed: one steep, bipolar-like switching between two degenerate polarization states; and another flat, multi-step switching process with a thermodynamically stable non-polar mesophase mediating the degenerate polarization states. The two are determined by the distinct Landau energy landscapes that are strongly dependent on the intrinsic domain configurations and interdomain interactions. This work bridges the gap between micro domain dynamics and macro polarization switching, providing a guiding principle for the strategic design and optimization of relaxors.

Fermion bound states from Yukawa coupling with periodic bosonic background

The Yukawa coupling of fermions with a periodic bosonic background is shown to give rise to several bound states to the fermionic spectrum, with some bound states gluing together around specific energy eingenvalues as the Yukawa coupling increases. This effect induces the presence of degenerate energy states inside the fermionic gap and may be of current interest.

Jahn-Teller and pseudo-Jahn-Teller effects on the vibronic structure of the photoionized spectrum of cyanopropyne.

Nonadiabatic quantum dynamics are carried out to illustrate the photoionized spectrum of the cyanopropyne (CH3-C≡C-C≡N) as reported in recent experimental measurements [Lamarre et al., J. Mol. Spectrosc. 315, 206 (2015)]. A detailed electronic structure calculation is performed to analyze the topographical details of the first five ionized states, of which three are degenerate states (X̃2E, B̃2E, and C̃2E) and two are non-degenerate states (Ã2A1 and D̃2A1). The degenerate E states of the C3V symmetry molecule are prone to Jahn-Teller (JT) instability, and in addition, symmetry allowed A1 - E vibronic coupling, i.e., pseudo-Jahn-Teller (PJT), effects are expected to have a significant impact in the detailed vibronic structure of these electronic states. The JT splittings of X̃2E and B̃2E degenerate states are small, whereas it is quite large at three high frequencies in the C̃2E electronic states. The large energy separation of X̃2E from the other states and the non-zero PJT coupling of the B̃2E state with the close-lying Ã2A1 state indicate the uncoupled nature of the X̃, Ã, and B̃ vibronic bands of C4H3N. The intersection minima of B̃ and C̃ states with the D̃ state nearly coincide with the energetic minimum of D̃ state. Therefore, the PJT couplings among these states will lead to a strong vibronic interaction to shape the respective band structure. To completely understand the JT and PJT interactions in the photoionized spectrum of C4H3N, the vibronic coupling model Hamiltonian was constructed to perform nuclear dynamics studies for these electronic states. The vibrational progressions in each vibronic band are identified and compared with the available experimental data in the literature. The impacts of JT and PJT effects in the first five ionized states of cyanopropyne are investigated and discussed in detail.

Internal Electric Fields and Structural Instabilities in Insulating Transition Metal Compounds: Influence on Optical Properties

AbstractThis work reviews new ideas developed in the last two decades which play a key role for understanding the optical properties of insulating materials containing transition metal (TM) cations. Initially, this review deals with compounds involving d4 and d9 ions where the local structure of the involved MX6 complexes (M=dn cation, X=ligand) is never cubic but distorted, a fact widely ascribed to the Jahn‐Teller (JT) effect. Nevertheless, that assumption is often wrong as the JT coupling requires an orbitally degenerate ground state in the initial geometry a condition not fulfilled even if the lattice is tetragonal. For this reason, the equilibrium geometry of d4 and d9 complexes in low symmetry lattices, is influenced by two factors: (i) The effects, usually ignored, of the internal electric field, ER, due to the rest of lattice ions on the active electrons localized in the MX6 unit. (ii) The existence of structural instabilities driven by vibronic interactions that lead to negative force constants. As first examples of these ideas, we show that the equilibrium structure, electronic ground state of KZnF3:Cu2+, K2ZnF4:Cu2+ and K2CuF4 obey to different causes and only in KZnF3:Cu2+ the JT effect takes place. These ideas also explain the local structure and optical properties of CuF2, CrF2 or KAlCuF6 compounds where the JT effect is symmetry forbidden and those of layered copper chloroperovskites where the orthorhombic instability explains the red shift of one d−d transition under pressure. In a second step, this review explores stable systems involving d3, d5 or d9 cations, where the internal electric field, ER, is responsible for some puzzling phenomena. This is the case of ruby and emerald that surprisingly exhibit a different color despite the Cr3+‐O2− distance is the same. A similar situation holds when comparing the normal (KMgF3) and the inverted (LiBaF3) perovskites doped with Mn2+ having the same Mn2+‐F distance but clearly different optical spectra. The role of ER is particularly remarkable looking for the origin of the color in the historical Egyptian Blue pigment based on CaCuSi4O10.

Experimental observation of super-Klein tunneling in phononic crystals

We numerically and experimentally report the acoustic analogue of the super-Klein tunneling in a heterojunction of phononic crystals formed with Willis scatterers that exhibit pseudospin-1 Dirac cones. Pseudospin-1 Dirac cones are characterized by a triple states degeneracy in the band structure where two linear bands intersect with a flatband. The scattering properties of pseudospin-1 quasiparticles comprise an unity transmission through one potential barrier at its center frequency for all incident angles, which is called the super-Klein tunneling. In addition, the unity transmission does not depend on the barrier width. The Super-Klein tunneling differs from the conventional Klein tunneling, which consists of perfect transmission only under normal incidence through a potential barrier of any width. The Klein tunneling is predicted in pseudospin-1/2 systems like graphene, which are characterized by a two states degeneracy with two intersecting linear band. This direct observation in this acoustic analogue may have important implications in the exploration of the rich physics of pseudospin-1 quasiparticles.