Spin Symmetry Research Articles

PCMW2D and 2D Raman correlation spectroscopy evidence for presence of spin-phonon coupling in hexagonal LuMnO3

Two-dimensional correlation spectroscopy (2D-COS) and perturbation-correlation moving window two-dimensional correlation spectroscopy (PCMW2D) analysis are performed on the temperature-dependent Raman spectra of hexagonal LuMnO3 single crystal. Under the resonance with the on-site Mn d-d transitions, the correlation between the phonons which are relate to the vibration of Mn ions’ bonds and spin-excitation peaks suggest a strong spin-phonon coupling in LuMnO3. The PCMW2D results clearly show that the significant change in phonons and spin-excitation peaks occurs around the Néel temperature and the spin reorientation transition. The multiple components in the broad spin-excitation peaks also suggest variations in spin symmetries in the ground state. Furthermore, we propose that the 2D-COS and PCMW2D Raman correlation spectroscopies provide a simple and powerful method for investigating the couplings and the transitions, which would be very important for understanding systematically the magnetoelectric properties of multiferroic materials.

Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations

The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. Here, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, the latter help to reduce unnecessary circuit excitations and thus accelerate the optimization process enabling researchers to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two orders of magnitude with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.

Quintuple Function Integration in Two-Dimensional Cr(II) Five-Membered Heterocyclic Metal Organic Frameworks via Tuning Ligand Spin and Lattice Symmetry.

Two-dimensional (2D) semiconductors (SCs) integrated with two or more functions are the cornerstone for constructing multifunctional nanodevices but remain largely limited. Here, by tuning the spin state of organic linkers and the symmetry/topology of crystal lattices, we predict a class of unprecedented multifunctional SCs in 2D Cr(II) five-membered heterocyclic metal organic frameworks that simultaneously possess auxetic effect, room-temperature ferrimagnetism, chiral ferroelectricity (FE), electrically reversible spin polarization, and topological nodal lines/points. Taking 2D Cr(TDZ)2 (TDZ = 1.2.5-thiadiazole) as an exemplification, the auxetic effect is produced by the antitetra-chiral lattice structure. The high temperature ferrimagnetism originates from the strong d-p direct magnetic exchange interaction between Cr cations and TDZ doublet radical anions. Meanwhile, the clockwise-counterclockwise alignment of TDZ's dipoles results in unique 2D chiral FE with atomic-scale vortex-antivortex states. 2D Cr(TDZ)2 is an intrinsic bipolar magnetic SC where half-metallic conduction with switchable spin-polarization direction can be induced by applying a gate voltage. In addition, the symmetry of the little group C4 of the lattice structure endows 2D Cr(TDZ)2 with topological nodal lines and a quadratic nodal point in the Brillouin zone near the Fermi level.

Restoring broken symmetries using quantum search “oracles”

We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search algorithms. We show how to construct the oracle and the projector associated with a symmetry operator. The procedure is illustrated for the parity, particle number, and total spin symmetries. The oracle is used to restore symmetry by indirect measurements using a single ancillary qubit. An illustration of the technique is made to obtain the approximate ground state energy for the pairing model Hamiltonian.

Systematically improvable mean-field variational ansatz for strongly correlated systems: Application to the Hubbard model

A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature ${T}_{\mathrm{eff}}$ is defined, probing the distance of the ground-state properties of the model in the thermodynamic limit from the ones of the proposed correlated mean-field ansatz. In this way, their uncertainties from the unbiased zero temperature limit may be estimated by simple and stable extrapolations well before the so-called sign problem gets prohibitive. At finite ${T}_{\mathrm{eff}}$, the convergence of the energy to the thermodynamic limit is indeed shown to already be possible in the Hubbard model for relatively small square lattices with linear dimension $L\ensuremath{\simeq}10$, thanks to appropriate averages over several twisted boundary conditions. Within the estimated energy accuracy of the proposed variational ansatz, two clear phases are identified, as the energy is lowered by spontaneously breaking some symmetries satisfied by the Hubbard Hamiltonian: (a) a stripe phase where both spin and translation symmetries are broken and (b) a strong coupling $d$-wave superconducting phase when the particle number is not conserved and global $U(1)$ symmetry is broken. On the other hand, the symmetric phase is stable in a wide region at large doping and small coupling.

Relativistic energies and information entropy of the inversely quadratic Hellmann potential

The solutions to the Dirac equation are obtained in the spin and pseudospin symmetry limits are presented using the parametric Nikiforov-Uvarov (pNU) method with the inversely quadratic Hellman (IQH) potential. In the exact non-relativistic spin symmetry limit, the energy and wave function of the IQH potential are obtained and used to investigate the Shannon information entropy of the system. Numerical results of the relativistic energies of the spin and pseudospin symmetry limits of the Dirac equation with the IQH potential are presented and observed to exhibit degeneracy. Also, the results of the Shannon entropy for six states (n = 0, 1, 2, 3, 4, 5) show that the momentum space wave function and probability density are better localized than the position space wave function. Also, the Bialynicki-Birula and Mycielski (BBM) inequality is verified for the system. Our results are found to be consistent with those previously reported in the literature.

Rashba spin-orbit coupling in the square-lattice Hubbard model: A truncated-unity functional renormalization group study

The Rashba-Hubbard model on the square lattice is the paradigmatic case for studying the effect of spin-orbit coupling, which breaks spin and inversion symmetry, in a correlated electron system. We employ a truncated-unity variant of the functional renormalization group which allows us to analyze magnetic and superconducting instabilities on equal footing. We derive phase diagrams depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor hopping, and electron filling. We find commensurate and incommensurate magnetic phases which compete with $d$-wave superconductivity. Due to the breaking of inversion symmetry, singlet and triplet components mix; we quantify the mixing of $d$-wave singlet pairing with $f$-wave triplet pairing.

Calculation of molecular g-tensors by sampling spin orientations of generalised Hartree-Fock states

The variational inclusion of spin–orbit coupling in self-consistent field (SCF) calculations affords single-determinant wave functions that completely break spin symmetry. The individual components of the molecular g-tensor are commonly obtained from separate SCF solutions that align the magnetic moment along one of the three principal tensor axes. However, this strategy raises the question if energy differences between solutions are relevant, or how convergence is achieved if the principal axis system is not determined by molecular symmetry. The present work resolves these issues by a simple two-step procedure akin to the generator coordinate method (GCM). First, the orientation of the magnetic moment is constrained in generalised Hartree-Fock (GHF) calculations. Then, non-orthogonal configuration interaction between GHF determinants yields a Kramers doublet for the calculation of the complete g-tensor. Alternatively, diagonalisation in a basis spanned by spin rotations of a single GHF determinant results in qualitatively correct g-tensors by eliminating errors related to spin contamination. For small first-row molecules, these approaches are evaluated against experimental data and full configuration interaction results. It is further demonstrated for two fictitious tetrahedral and species that a GCM strategy can describe the spin–orbit splitting of orbitally-degenerate ground states, which may lead to negative g-values.

Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity

Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density of states of multilayer graphene with up to four layers at the single-particle band structure level in the presence of a transverse electric field. Among the considered structures, tetralayer graphene with rhombohedral (ABCA) stacking reaches the highest density of states. We study the phases that can arise in ABCA graphene by tuning the carrier density and transverse electric field. For a broad region of the tuning parameters, the presence of strong Coulomb repulsion leads to a spontaneous spin and valley symmetry breaking via Stoner transitions. Using a model that incorporates the spontaneous spin and valley polarization, we explore the Kohn-Luttinger mechanism for superconductivity driven by repulsive Coulomb interactions. We find that the strongest superconducting instability is in the $p-$wave channel, and occurs in proximity to the onset of Stoner transitions. Interestingly, we find a range of densities and transverse electric fields where superconductivity develops out of a strongly corrugated, singly-connected Fermi surface in each valley, leading to a topologically non-trivial chiral $p+ip$ superconducting state with an even number of co-propagating chiral Majorana edge modes. Our work establishes ABCA stacked tetralayer graphene as a promising platform for observing strongly correlated physics and topological superconductivity.

Evidence for Topological Magnon-Phonon Hybridization in a 2D Antiferromagnet down to the Monolayer Limit.

Topological phonons and magnons potentially enable low-loss, quantum coherent, and chiral transport of information and energy at the atomic scale. Van der Waals magnetic materials are promising to realize such states due to their recently discovered strong interactions among the electronic, spin, and lattice degrees of freedom. Here, we report the first observation of coherent hybridization of magnons and phonons in monolayer antiferromagnet FePSe3 by cavity-enhanced magneto-Raman spectroscopy. The robust magnon-phonon cooperativity in the 2D limit occurs even in zero magnetic field, which enables nontrivial band inversion between longitudinal and transverse optical phonons caused by the strong coupling with magnons. The spin and lattice symmetry theoretically guarantee magnetic-field-controlled topological phase transition, verified by nonzero Chern numbers calculated from the coupled spin-lattice model. The 2D topological magnon-phonon hybridization potentially offers a new route toward quantum phononics and magnonics with an ultrasmall footprint.

Spin and Orbital Symmetry Breakings Central to the Laser-Induced Ultrafast Demagnetization of Transition Metals

The role of spin and orbital rotational symmetry on the laser-induced magnetization dynamics of itinerant-electron ferromagnets was theoretically investigated. The ultrafast demagnetization of transition metals is shown to be the direct consequence of the fundamental breaking of these conservation laws in the electronic system, an effect that is inherent to the nature of spin-orbit and electron-lattice interactions. A comprehensive symmetry analysis is complemented by exact numerical calculations of the time evolution of optically excited ferromagnetic ground states in the framework of a many-body electronic Hamiltonian. Thus, quantitative relations are established between the strength of the interactions that break the rotational symmetries and the time scales that are relevant for the magnetization dynamics.

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

Nonequilibrium situations where selected currents are suppressed are of interest in fields like thermoelectrics and spintronics, raising the question of how the related noises behave. We study such zero-current charge, spin, and heat noises in a two-terminal mesoscopic conductor. In the presence of voltage, spin, and temperature biases, the nonequilibrium (shot) noises of charge, spin, and heat can be arbitrarily large, even if their average currents vanish. However, as soon as a temperature bias is present, additional equilibrium (thermal-like) noise necessarily occurs. We show that this equilibrium noise sets an upper bound on the zero-current charge and spin shot noises, even if additional voltage or spin biases are present. We demonstrate that these bounds can be overcome for heat transport by breaking the spin and electron-hole symmetries, respectively. By contrast, we show that the bound on the charge noise for strictly two-terminal conductors even extends into the finite-frequency regime.

Emergence of heavy quark spin symmetry breaking in heavy quarkonium decays

Heavy-quark spin symmetry (HQSS) implies that in the direct decay of a heavy quarkonium with spin $S$, only lower lying heavy quarkonia with the same spin $S$ can be produced. However, this selection rule, expected to work very well in the $b$-quark sector, can be overcome if multiquark intermediate states are involved in the decay chain, allowing for transitions to the final-state heavy quarkonia with a different spin ${S}^{\ensuremath{'}}$. In particular, the measured decays $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3) and $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}{h}_{b}(mP)$ ($m=1$, 2) appear to have nearly equal strengths, which is conventionally explained by a simultaneous presence of both ${S}_{b\overline{b}}=0$ and ${S}_{b\overline{b}}=1$ components in the wave functions of the ${Z}_{b}\mathrm{s}$ in equal shares. Meanwhile, the destructive interference between the contributions of the ${Z}_{b}$ and ${Z}_{b}^{\ensuremath{'}}$ to the decay amplitude for a $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ final state kills the signal to zero in the strict HQSS limit. In this paper, we discuss how the HQSS violation needs to be balanced by the narrowness of the ${Z}_{b}^{(\ensuremath{'})}$ states in the physical case to allow for equal transition strengths into final states with different total heavy quark spins, and how spin symmetry is restored as a result of a subtle interplay of the scales involved, when the mass of a heavy quark becomes infinite. Moreover, we demonstrate how similar branching fractions of the decays into $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ and $\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}$ can be obtained and how the mentioned HQSS breaking can be reconciled with the dispersive approach to the $\ensuremath{\pi}\ensuremath{\pi}/K\overline{K}$ interaction in the final state and matched with the low-energy chiral dynamics in both final states.

Instanton gas approach to the Hubbard model

In this paper, we consider a path integral formulation of the Hubbard model based on a Hubbard-Stratonovich transformation that couples the auxiliary field to the local electronic density. This decoupling is known to have a saddle-point structure that shows a remarkable regularity: The field configuration at each saddle point can be understood in terms of a set of elementary field configurations localized in space and imaginary time which we coin instantons. The interaction between instantons is short ranged. Here, we formulate a classical partition function for the instanton gas that has predictive power. For a given set of physical parameters, we can predict the distribution of instantons and show that the instanton number is sharply defined in the thermodynamic limit, thereby defining a unique dominant saddle point. Decoupling in the charge channel conserves SU(2) spin symmetry for each field configurations. Hence, the instanton approach provides an SU(2) spin-symmetric approximation to the Hubbard model. It fails, however, to capture the magnetic transition inherent to the Hubbard model on the honeycomb lattice despite being able to describe local moment formation. In fact, the instanton itself corresponds to local moment formation and concomitant short-ranged antiferromagnetic correlations. This aspect is also seen in the single particle spectral function that shows clear signs of the upper and lower Hubbard bands. Our instanton approach bears remarkable similarities to local dynamical approaches, such as dynamical mean-field theory, in the sense that it has the unique property of allowing for local moment formation without breaking the SU(2) spin symmetry. In contrast to local approaches, it captures short-ranged magnetic fluctuations. Furthermore, it also offers possibilities for systematic improvements by taking into account fluctuations around the dominant saddle point. Finally, we show that the saddle point structure depends upon the choice of lattice geometry. For the square lattice at half filling, the saddle-point structure reflects the itinerant to localized nature of the magnetism as a function of the coupling strength. The implications of our results for Lefschetz thimble approaches to alleviate the sign problem are also discussed.

Beyond the Standard Model with Six-Dimensional Spinors

Six-dimensional spinors with Spin(3,3) symmetry are utilized to efficiently encode three generations of matter. E8(−24) is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, SU(5), and Spin(10) grand unified theories are found when a single generation is isolated. For spacetime symmetries, Spin(4,2) may be used for conformal symmetry, AdS5→dS4, or simply broken to Spin(3,1) of a Minkowski space. Another class of representations finds Spin(2,2) and can give AdS3 with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor 128 of Spin(4,12) is found with Spin(3) flavor symmetry inside E8(−24). The 128 of Spin(12,4) can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane E8(−24)/Spin(12,4)=(OsxO)P2.

U -spin puzzle in B decays

We impose $U$-spin symmetry [$SU(2{)}_{\text{Uspin}}$] on the Hamiltonian for $B$ decays. As expected, we find the equality of amplitudes related by the exchange $d\ensuremath{\leftrightarrow}s$. We also find that the amplitudes for the $\mathrm{\ensuremath{\Delta}}S=0$ processes ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{\ensuremath{-}}$, and ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ form a $U$-spin triangle relation. The amplitudes for ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$, ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{K}^{+}$, and ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ form a similar $\mathrm{\ensuremath{\Delta}}S=1$ triangle relation. And these two triangles are related to one another by $d\ensuremath{\leftrightarrow}s$. We perform fits to the observables for these six decays. If perfect $U$ spin is assumed, then the fit is very poor. If $U$-spin-breaking contributions are added, then we find many scenarios that can explain the data. However, in all cases, 100% $U$-spin breaking is required, considerably larger than the naive expectation of $\ensuremath{\sim}20%$. This is the $U$-spin puzzle; it may be strongly hinting at the presence of new physics.

Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm.

In the nonrelativistic Schrödinger equation, the total spin S and spin projection M are good quantum numbers. In contrast, spin symmetry is lost in the presence of spin-dependent interactions, such as spin-orbit couplings in relativistic Hamiltonians. Therefore, the relativistic density matrix renormalization group algorithm (R-DMRG) only employing particle number symmetry is much more expensive than nonrelativistic DMRG. In addition, artificial breaking of Kramers degeneracy can happen in the treatment of systems with an odd number of electrons. To overcome these issues, we propose time-reversal symmetry adaptation for R-DMRG. Since the time-reversal operator is antiunitary, this cannot be simply achieved in the usual way. We introduce a time-reversal symmetry-adapted renormalized basis and present strategies to maintain the structure of basis functions during the sweep optimization. With time-reversal symmetry adaptation, only half of the renormalized operators are needed, and the computational costs of Hamiltonian-wavefunction multiplication and renormalization are reduced by half. The present construction of the time-reversal symmetry-adapted basis also directly applies to other tensor network states without loops.

Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models

We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of $T_c$ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in $T_c$ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.

P_{cc}^N states in a unitarized coupled-channel approach

Starting from an effective Lagrangian with heavy quark spin symmetry embedded, the coupled-channel dynamics of the doubly charmed systems D^{(*)} Sigma _c^{(*)} is investigated. The potential underlying our investigation includes t-channel pseudoscalar and vector meson exchanges. A series of S-wave bound states with isospin I=1/2 is found by applying the first iterated solution of the N/D method: one state with binding energy 23 MeV in the 5/2^-D^*Sigma _c^* channel, three states with binding energy 26, 30 and 7 MeV (relative to the thresholds from low to high, respectively) in the 3/2^-DSigma _c^*-D^*Sigma _c-D^*Sigma _c^* system and three states with binding energy 32, 8 and 16 MeV in the 1/2^-DSigma _c-D^*Sigma _c-D^*Sigma _c^* system. Those P_{cc}^N states serve as the open-charm partners of the hidden charm pentaquarks P_{psi }^N observed by the LHCb Collaboration.

Dirac Equation for Energy-Dependent Potential With Energy-dependent Tensor Interaction

The relativistic symmetries of the Dirac equation were investigated with an energy-dependent tensor potential interaction for two different energy-dependent potentials under parametric Nikiforov-Uvarov method and supersymmetric quantum mechanics and shape-invariance method. It is observed that the energy-dependent tensor interaction has stronger removal effect of the energy degeneracies in both the spin and pseudospin symmetries than the non-energy-dependent tensor interaction.