Spin Symmetry Breaking Research Articles

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C36 Fullerene and an Iron Porphyrin Model Complex.

We present three distinct examples where phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wave function with essential symmetry breaking. Essential symmetry breaking was first introduced by Lee and Head-Gordon [ Phys. Chem. Chem. Phys. 2019, 21, 4763-4778, 10.1039/C8CP07613H]. We utilized essential complex and time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the singlet-triplet gap of a known biradicaloid, C36. ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C36. Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single-determinant trial wave function with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

Spin symmetry breaking and entropy production during the evolution of spinor Bose-Einstein condensate driven by coherent atom beam

This paper predicts a spontaneous symmetry breaking in the time evolution of a mesoscopic condensate with degenerate internal degrees of freedom, driven by a coherent atom beam. Both entanglement entropy and the statistical entropy peak at the critical time when the spontaneous symmetry breaking takes place. The condensate approaches a steady state that is dictated by the incident atom beam, providing a way to control the distribution of internal degrees of freedom.

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

For the first time, the theoretical model of the spin-electron structure of a singlelayer graphene film was proposed by Wallace. The literature also describes ferromagnetism generated by none of the three common causes: impurities, defects, boundaries. We believe that the source of ferromagnetism is the spontaneous breaking of spin symmetry in a graphene film. The classical field model describing spontaneously broken symmetry is necessarily non-linear. Among non-linear models, the simplest is the well-known 4 model. We believe that, as a first approximation, we can describe with its help all the characteristics of spin waves that interest us, their spectra, and the domain structure of ferromagnetism in graphene. The model admits kink and anti-kink exact solutions and a quasiparticle breather, which we modeled numerically. We use the kink-anti-kink interaction energy obtained numerically to solve the Schrödinger equation, which simulates the quantum dynamics of breathers, which underlies the description of spin waves. The solution of the Schrödinger equation by the Ritz method leads to a generalized problem of eigenvalues and eigenvectors, the solution of which is mainly devoted to this work.

Symmetry in Multiple Self-Consistent-Field Solutions of Transition-Metal Complexes.

We use a method based on metadynamics to locate multiple low-energy Unrestricted Hartree-Fock (UHF) self-consistent-field (SCF) solutions of two model octahedral d1 and d2 transition-metal complexes, [MF6]3- (M = Ti, V). By giving a group-theoretical definition of symmetry breaking, we classify these solutions in the framework of representation theory and observe that a number of them break spin or spatial symmetry, if not both. These solutions seem unphysical at first, but we show that they can be used as bases for Non-Orthogonal Configuration Interaction (NOCI) to yield multideterminantal wave functions that have the right symmetry to be assigned to electronic terms. Furthermore, by examining the natural orbitals and occupation numbers of these NOCI wave functions, we gain insight into the amount of static correlation that they incorporate. We then investigate the behaviors of the most low-lying UHF and NOCI wave functions when the octahedral symmetry of the complexes is lowered and deduce that the symmetry-broken UHF solutions must first have their symmetry restored by NOCI before they can describe any vibronic stabilization effects dictated by the Jahn-Teller theorem.

Coupled alkali halide color centers: Fractional charge errors, fractional spin errors, and a failure of spin symmetry breaking produce challenging tests for condensed-phase electronic structure calculations

Color centers (F-centers) consist of defect-trapped electrons confined and shielded by a surrounding ionic lattice. This work shows how adjacent color centers in lithium fluoride provide a suite of challenging tests for electronic structure calculations in condensed phases, mimicking theoretically well-studied but experimentally fleeting gas-phase model systems such as stretched H2+, stretched H2, and stretched H3+. Singlet-triplet gaps and electron transfer reactions among these centers exhibit delocalization (fractional charge), strong left-right correlation (fractional spin), and a density-driven failure of spin-symmetry-broken singlet calculations. Tests of representative density functional theory approximations show that new “non-zero-sum” approaches qualitatively improve agreement with correlated multireference benchmark values.

Spin Symmetry Breaking in the Translation-Invariant Hartree--Fock Electron Gas

We study the breaking of spin symmetry for the nonlinear Hartree-Fock model describing an infinite translation-invariant interacting quantum gas (fluid phase). At zero temperature and for the Coulomb interaction in three space dimensions, we can prove the existence of a unique first order transition between a pure ferromagnetic phase at low density and a paramagnetic phase at high density. Multiple first or second order transitions can happen for other interaction potentials, as we illustrate on some examples. At positive temperature T>0 we compute numerically the phase diagram in the Coulomb case. We find the paramagnetic phase at high temperature or high density and a region where the system is ferromagnetic. We prove that the equilibrium measure is unique and paramagnetic at high temperature or high density.

Cubic hastatic order in the two-channel Kondo-Heisenberg model

Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with $\Gamma_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields.

Exclusive decays $\chi_{cJ}\rightarrow K^{\ast} (892)K$ χ c J → K * ( 892 ) K within the effective field theory framework

We study hadronic decays $\chi_{cJ}\rightarrow K^*(892)\bar{K} $ within the effective field theory framework. We consider the colour-singlet and colour-octet contributions and study their properties using (p)NRQCD effective theory. We show that infrared singularities in collinear integrals of the colour-singlet amplitudes can be absorbed into the renormalisation of the colour-octet matrix elements. The heavy quark spin symmetry allows us to establish a relation between the colour-octet matrix elements and to define the spin symmetry breaking corrections which are free from infrared singularities. We apply obtained results for a phenomenological description of the branching fractions.

Qualitative Views on the Polyradical Character of Long Acenes.

Spin-symmetry breaking appears in the DFT treatment of polyacenes, beyond a certain length, the critical length depending on the exchange-correlation potential. This phenomenon may be attributed to an instability with respect to HOMO-LUMO mixing, which suggests a diradical character of long acenes. However, the increase of the S2 operator with acene length questions this simple view. It is shown that this increase cannot be attributed to spin polarization of the inner MOs, and that a second symmetry breaking takes place for the pentadecacene, with four unpaired electrons centered at the first and third quarters of the chain. The spin density distributions of broken-symmetry solutions support a qualitative picture in terms of tetra-methylene hexacenes separated by Clar sextets. A strategy is proposed to identify local symmetry breaking in polyradical systems.

Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry

Graphene is considered a specific object whose electronic structural features are presented in the light of the general concept of emergent phenomena that arise as a result of a quantum phase transition caused by the breaking of continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electron subsystem caused by the correlation of its odd pz-electrons that depends on the distance between these electrons and becomes noticeable when the shortest distance, determined by the C = C bond length, exceeds the critical magnitude Rcr = 1.395 Å. The symmetry breaking is reliably predicted by the unrestricted Hartree–Fock (UHF) formalism, which provides a sufficient level of quantitative self-consistent description for the problem. Empirical support has been given to and reliable certification obtained for UHF emergents such as (i) open-shell electron spin-orbitals; (ii) splitting and/or spin polarization of electron spectra; (iii) a spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states, and (iv) the existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other sp2 nanocarbons and not only gives a clear insight into the spin features of graphene chemistry, accentuating its emergent character, but also expectedly predicts the occurrence of new graphene physics-related emergents. In the latter case, symmetry breaking is relevant for both the spin system and time reversal and imposes on graphene special physical properties such as ferromagnetism, superconductivity, and topological nontriviality. This review shows, for the first time, that not only the ferromagnetism but also the mechanical properties of graphene are essentially emergent, extending this feature to the entire physics of graphene.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields.

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient-quantified through the anapole moments-of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree–Fock Theory

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ2 and Ŝ3) symmetry breaking properties. When imposing Ŝ2 and Ŝ3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ2 and Ŝ3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

DFT calculations of strain and interface effects on electronic structures and magnetic properties of L1-FePt/Ag heterojunction of GMR applications

In this work, density functional theory (DFT) was employed to investigate the effect of strain and interface on electronic structures and magnetic properties of L10-FePt/Ag heterojunction. Two possible interface structures of L10-FePt(001)/Ag(001), that is, interface between Fe and Ag layers (Fe/Ag) and between Pt and Ag layers (Pt/Ag), were inspected. It was found that Pt/Ag interface is more stable than Fe/Ag interface due to its lower formation energy. Further, under the lattice mismatch induced tensile strain, the enhancement of magnetism for both Fe/Ag and Pt/Ag interface structures has been found to have progressed, though the magnetic moments of “interfacial” Fe and Pt atoms have been found to have decreased. To explain this further, the local density of states (LDOS) analysis suggests that interaction between Fe (Pt) and Ag near Fe/Ag (Pt/Ag) interface leads to spin symmetry breaking of the Ag atom and hence induces magnetism magnitude. In contrast, the magnetic moments of interfacial Fe and Pt atoms reduce because of the increase in the electronic states near the Fermi level of the minority-spin electrons. In addition, the significant enhancements of the LDOS near the Fermi levels of the minority-spin electrons signify the boosting of the transport properties of the minority-spin electrons and hence the spin-dependent electron transport at this ferromagnet/metal interface. From this work, it is expected that this clarification of the interfacial magnetism may inspire new innovation on how to improve spin-dependent electron transport for enhancing the giant magnetoresistance (GMR) ratio of potential GMR-based spintronic devices.

Time-dependent broken-symmetry density functional theory simulation of the optical response of entangled paramagnetic defects: Color centers in lithium fluoride

Parameter-free atomistic simulations of entangled solid-state paramagnetic defects may aid in the rational design of devices for quantum information science. This work applies time-dependent density functional theory (TDDFT) embedded-cluster simulations to a prototype entangled-defect system, namely two adjacent singlet-coupled $F$ color centers in lithium fluoride. TDDFT calculations accurately reproduce the experimental visible absorption of both isolated and coupled $F$ centers. The most accurate results are obtained by combining spin symmetry breaking to simulate strong correlation, a large fraction of exact (Hartree-Fock-like) exchange to minimize the defect electrons' self-interaction error, and a standard semilocal approximation for dynamical correlations between the defect electrons and the surrounding ionic lattice. These results motivate application of two-reference correlated ab initio approximations to the M-center, and application of TDDFT in parameter-free simulations of more complex entangled paramagnetic defect architectures.

Predicting the Open-Shell Character of Polycyclic Hydrocarbons in Terms of Clar Sextets.

Rather unexpected spin-symmetry breakings of mean-field single determinants occur in singlet ground states of many families of alternating conjugated hydrocarbons which accept a full on-bond electron pairing. These symmetry breakings may be seen as an indication of the existence of unpaired electrons. Although qualitative, the concept of disjoint electronic sextets proposed by Clar (hereafter called CS) is at least a heuristic tool for predicting various features of fused polybenzenic hydrocarbons. The present work shows that identifying the preferred CS distribution enables one to rationalize the existence of one or several spin-symmetry breakings, i.e., the existence and the number of unpaired electrons in alternant fused polycyclic hydrocarbons via a simple recipe for the prediction of these features. This recipe is based on comparison between various distributions of CS on the molecular frame, subject to a restriction concerning the fragments of the graph that do not belong to the CS. This rule is successfully confronted to UDFT calculations and to a recently proposed criterion predicting the possible occurrence of spin-symmetry breaking from the topological Hückel Hamiltonian. The confrontation runs on series of rhombuses, periacenes, anthenes, and other graphene flakes or nanoribbons. The CS distribution definitely offers a qualitative guide to look at the possible occurrence of (multiple) symmetry breakings in polycyclic architectures which are commonly seen as closed-shell singlets.

Dirac Material Graphene

Abstract The paper presents an overview of graphene electronic structure in light of a general concept of emergent phenomena that result from the quantum phase transition caused by continuous symmetry breaking. In the current case, the spin symmetry breaking is provided by a drastic enhancement of pz odd electron correlation when the shortest distance between them, defined by C=C bond length, exceeds critical value Rcri. The UHF formalism clearly evidences the broken symmetry occurrence and perfectly suits to self-consistent description of the issue. Empirically supported and convincingly certified, the UHF emergents, such as (i) open-shell character of electron spinorbitals; (ii) spin polarization of electron spectrum; (iii) spin contamination; (iv) depriving the spin multiplicity of electronic states; (v) local spin pool at zero total spin density, and so forth greatly extend the view on ground states of graphene and other sp2 nanocarbons and not only give a clear vision of spin peculiarities of graphene chemistry but predicatively point to the occurrence of emergents related to graphene physics, such as ferromagnetism, superconductivity and topological nontriviality. The paper presents numerous experimental evidences supporting a deep interrelationship between emergent chemistry and emergent physics of graphene.

Simple Model of Nonlinear Spin Waves in Graphene Structures

A series of theoretical and experimental works is known which investigated the magnetic properties of graphene structures. This is due, among other things, to the prospects of using graphene as a material for the needs of the future nanoelectronics and spintronics. In particular, it is known about the presence of ferromagnetic properties at temperatures up to 200 C and above in a single-layer graphene films that are free from impurities. Previously there was proposed a quantum field theoretical model describing the possible mechanism of ferromagnetism in graphene as a result of spontaneous breaking of spin symmetry of the surface density of valence electrons. The possible spatial configurations of the localized spin density were described. In this paper we investigate such spatially localized nonlinear spin configurations of the valence electron density on the graphene surface such as kinks, and their interactions, as well as quasibound metastable states of the interacting kinks and antikinks, that are breathers. The spectrum of such breathers is investigated. It is shown that under certain conditions, this spectrum has a discrete sector, which, in turn, allows us to speak about the possibility of coherent quantum generation of spin waves in graphene structures, which is important in terms of practical applications in nanoelectronics and spintronics.

One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces

In this work we demonstrate that the heat bath configuration interaction (HCI) and its semistochastic extension can be used to treat relativistic effects and electron correlation on an equal footing in large active spaces to calculate the low energy spectrum of several systems including halogen group atoms (F, Cl, Br, I), coinage atoms (Cu, Au), and the neptunyl(VI) dioxide radical. This work demonstrates that despite a significant increase in the size of the Hilbert space due to spin symmetry breaking by the spin-orbit coupling terms, HCI retains the ability to discard large parts of the low importance Hilbert space to deliver converged absolute and relative energies. For instance, by using just over 107 determinants we get converged excitation energies for Au atom in an active space containing (150o,25e) which has over 1030 determinants. We also investigate the accuracy of five different two-component relativistic Hamiltonians in which different levels of approximations are made in deriving the one-electron and two-electrons Hamiltonians, ranging from Breit-Pauli (BP) to various flavors of exact two-component (X2C) theory. The relative accuracy of the different Hamiltonians are compared on systems that range in atomic number from first row atoms to actinides.

Disorder-induced optical transition from spin Hall to random Rashba effect.

Disordered structures give rise to intriguing phenomena owing to the complex nature of their interaction with light. We report on photonic spin-symmetry breaking and unexpected spin-optical transport phenomena arising from subwavelength-scale disordered geometric phase structure. Weak disorder induces a photonic spin Hall effect, observed via quantum weak measurements, whereas strong disorder leads to spin-split modes in momentum space, a random optical Rashba effect. Study of the momentum space entropy reveals an optical transition upon reaching a critical point where the structure's anisotropy axis vanishes. Incorporation of singular topology into the disordered structure demonstrates repulsive vortex interaction depending on the disorder strength. The photonic disordered geometric phase can serve as a platform for the study of different phenomena emerging from complex media involving spin-orbit coupling.

σ-SCF: A direct energy-targeting method to mean-field excited states.

The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry-a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states-ground or excited-are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.