Particle-hole Conjugation Research Articles

Topological Circular Dichroism in Chiral Multifold Semimetals.

Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2eV. Our Letter demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.

Anderson's Theorem for Correlated Insulating States in Twisted Bilayer Graphene.

The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under PT, where P and T denote particle-hole conjugation and time reversal, respectively. In contrast, PT-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states.

Pseudoscalar U(1) spin liquids in α−RuCl3

A recent experiment has reported oscillations of the thermal conductivity of $\alpha$-RuCl$_3$ driven by an in-plane magnetic field that are reminiscent of the quantum oscillations in metals. At first glance, these observations are consistent with the presence of the long-sought-after spinon Fermi surface state. Strikingly, however, the experiment also reported vanishing thermal Hall conductivity coexisting with the oscillations of the longitudinal one. Such absence of the thermal Hall effect must originate from crystalline symmetries of $\alpha$-RuCl$_3$. But if the system was a traditional spinon fermi surface state, these symmetries would also necessarily prohibit the emergence of a magnetic field acting on the spinons, in stark contradiction with the presence of quantum oscillations in experiments. To reconcile these observations, we introduce a new class of symmetry enriched ``pseudoscalar" U(1) spin liquids in which certain crystalline symmetries act as a particle-hole conjugation on the spinons. The associated pseudoscalar spinon Fermi surface states allow for the coexistence of an emergent Landau quantizing magnetic field while having an exactly zero thermal Hall conductivity. We develop a general theory of these states by constructing Gutzwiller-projected wave-functions and describing how they naturally appear as U(1) spin liquids with a distinctive projective symmetry group implementation of crystalline symmetries in the fermionic parton representation of spins. We propose that the field induced quantum disordered state in $\alpha$-RuCl$_3$ descends from a pseudoscalar spinon fermi surface state that features compensated spinon-particle and spinon-hole pockets possibly located around the $M$ points of its honeycomb Brillouin zone. These points are connected via a wave-vector associated with the emergence of the competing zig-zag antiferromagnetic state.

Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions

Particle-hole symmetry breaking in the fractional quantum Hall effect has recently been studied both theoretically and experimentally with most works focusing on non-Abelian states in the second electronic Landau level. In this work, we theoretically investigate particle-hole symmetry breaking of incompressible fractional quantum Hall states in the lowest Landau level under the influence of the realistic effect of a finite magnetic field strength. A finite magnetic field induces Landau level and sub-band mixing which are known to break particle-hole symmetry at the level of the Hamiltonian. We analyze the Haldane pseudopotentials, energy spectra and energy gaps, and the wave functions themselves, under realistic conditions. We find that particle-hole symmetry is broken, as determined by energy gaps, between states related via particle-hole conjugation, however, we find that particle-hole symmetry is largely maintained as determined by the effective mass of composite fermions. Finally, we comment and make connection to recent experimental observations regarding particle-hole symmetry in the lowest Landau level fractional quantum Hall effect [Pan et al. Phys. Rev. Lett. 124, 156801 (2020)]

Manifestation of the Berry phase in the atomic nucleus 213Pb

The neutron-rich 213Pb isotope was produced in the fragmentation of a primary 1 GeV A238U beam, separated in FRS in mass and atomic number, and then implanted for isomer decay γ-ray spectroscopy with the RISING setup at GSI. A newly observed isomer and its measured decay properties indicate that states in 213Pb are characterized by the seniority quantum number that counts the nucleons not in pairs coupled to angular momentum J=0. The conservation of seniority is a consequence of a geometric phase associated with particle-hole conjugation, which becomes observable in semi-magic nuclei where nucleons half-fill the valence shell. The γ-ray spectroscopic observables in 213Pb are thus found to be driven by two mechanisms, particle-hole conjugation and seniority conservation, which are intertwined through a Berry phase.

Particle–hole symmetries in condensed matter

The term “particle–hole symmetry” is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose to define the operation of “particle–hole conjugation” as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and we construct its invariant lift to the Fock space. Particle–hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle–hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. We illustrate that construction principle with a series of examples including the Su–Schrieffer–Heeger model and the Kitaev–Majorana chain. For an enhanced perspective, we contrast particle–hole symmetries with the charge-conjugation symmetry of relativistic Dirac fermions. We go on to present two major applications in the realm of interacting electrons. For one, we offer a heuristic argument that the celebrated Haldane phase of antiferromagnetic quantum spin chains is adiabatically connected to a free-fermion topological phase protected by a particle–hole symmetry. For another, we review the recent proposal by Son [Phys. Rev. X 5, 031027 (2015)] for a particle–hole conjugation symmetric effective field theory of the half-filled lowest Landau level, and we comment on the emerging microscopic picture of the composite fermion.

Non-Abelian twist to integer quantum Hall states

Through a theoretical coupled wire model, we construct strongly correlated electronic \emph{integer} quantum Hall states. As a distinguishing feature, these states support electric and thermal Hall transport violating the Wiedemann-Franz law as $\left(\kappa_{xy}/\sigma_{xy}\right)/\left[\left(\pi^{2}k_{B}^{2}T\right)/3e^{2}\right]<1$.We propose a new Abelian incompressible fluid at filling $\nu=16$ that supports a bosonic chiral $(E_{8})_{1}$ conformal field theory at the edge and is intimately related to topological paramagnets in (3+1)D. We further show that this topological phase can be partitioned into two non-Abelian quantum Hall states at filling $\nu=8$, each carrying bosonic chiral $(G_{2})_{1}$ or $(F_{4})_{1}$ edge theories, and hosting Fibonacci anyonic excitations in the bulk. Finally, we discover a new notion of particle-hole conjugation based on the $E_{8}$ state that relates the $G_{2}$ and $F_{4}$ Fibonacci states.

Edge-induced topological phase transition of the quantum Hall state at half filling

We show that in quantum Hall systems at half-filling, edge potentials alone can drive transitions between the Pfaffian and anti-Pfaffian topological phases. We conjecture this is true in realistic systems even in the presence of weak bulk interactions that break the particle-hole symmetry. The strong effects of edge potentials could be understood from different topological shifts of competing phases, manifested on the disk geometry as the variation of orbital numbers at fixed number of particles. In particular, we show analytically particle-hole conjugation of Hamiltonians on the disk is equivalent to the tuning of edge potentials, which allows us to explicitly demonstrate the phase transition numerically. The importance of edge potentials in various experimental contexts, including the recently discovered particle-hole symmetric phase is also discussed.

Particle-hole mirror symmetries around the half-filled shell: Quantum numbers and algebraic structure of composite fermions

Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are maximal. We identify the CF's quantum numbers as the angular momentum L in (L_e L_v)L, its magnetic projection m_L, the electron number N, with L_v={N-1)/2, and magnetic \nu-spin, m_\nu=L_e-L_v. Translationally invariant FQHE states are formed by filling p subshells with their respective CFs, in order of ascending L for fixed L_e and L_v, beginning with the lowest allowed value, L=|m_\nu|. We show that this wave function has an exactly equivalent hierarchical form. FQHE states can be grouped into \nu-spin multiplets mirror symmetric around m_\nu=0, with N held constant. Electron particle-hole conjugation with respect to this vacuum is identified as the mirror symmetry relating FQHE states of the same N but distinct fillings \nu = p/(2p+1} and p/( 2p-1). Alternatively, mirror symmetric \nu-spin multiplets can be constructed in which the magnetic field strength is held fixed: the valence states are electron particle-vortex hole excitations. Particle-hole symmetry -- relating the N-particle FQHE state of filling \nu=p/(2p+1} to the $\bar{N}$-particle state of filling {p+1)/(2p+1} -- is shown to be equivalent to electron-vortex exchange. In this construction $\bar{N}$-N CFs of the higher density state occupy an extra zero-mode subshell. We link this structure, familiar from supersymmetric quantum mechanics, to the CF Pauli Hamiltonian, which we show is isospectral, quadratic in the \nu-spin raising and lowering operators, and four-fold degenerate. On linearization, it takes a Dirac form similar to that found in the integer quantum Hall effect (IQHE).

Conservation laws in the1f7/2shell model ofCr48

Conservation laws in the $1f_{7/2}$ shell model of $^{48}$Cr found in numeric studies by Escuderos, Zamick and Bayman [A. Escuderos, L. Zamick, and B. F. Bayman, arXiv:0506050 (2005)] and me [K. Neerg\aa rd, Phys. Rev. C \textbf{90}, 014318 (2014)] are explained by symmetry under particle-hole conjugation and the structure of the irreps of the symplectic group Sp(4). A generalization is discussed.

Almost commuting matrices, localized Wannier functions, and the quantum Hall effect

For models of noninteracting fermions moving within sites arranged on a surface in three-dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are K-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward and does not require translational invariance or introduce a flux torus. We further show that there is a Z2 index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time-reversal or particle-hole conjugation. Finally, in the case of the sphere—mathematically speaking, three almost commuting Hermitians whose sum of square is near the identity—we give the first quantitative result, showing that this index is the only obstruction to finding commuting approximations. We review the known nonquantitative results for the torus.

Extended Time-Reversal Operator and the Symmetries of the Hyperon-Nucleon Interaction

An extended time-reversal operator incorporating charge conjugation in the flavor SU3 space is introduced in order to study the spin-flavor structure of the hyperon-nucleon inter­ action. Particle-hole conjugation in terms of this extended time reversal is found to be useful to characterize time-reversal odd components for the space-spin part of the hyperon-nucleon interaction, which yield non-zero contributions to the exchange Feynman diagram or to the transition amplitude between AN and EN systems when the flavor symmetry breaking is properly introduced. Some selection rules are also given for the spin-flavor factors appearing in the quark-model potentials of the hyperon-nucleon interaction. Since quantum chromo dynamics (QCD) was found to be the fundamental the­ ory of the strong interaction, a number of models have been proposed to understand nucleon-nucleon (N N) and hyperon-nucleon (Y N) interactions from more basic ele­ ments of quarks and gluons. Among these models, the non-relativistic quark model is in a unique position to enable us to take full account of the dynamical motion of the two composite baryons, though it can only describe confinement using a phe­ nomenological potential and it employs the quark-quark (qq) residual interaction derived from the color analogue of the Fermi-Breit interaction. Thanks to this ad­ vantage it can give a realistic description of the N Nand Y N interaction, if the missing meson-exchange effect, which dominates at the long-range part of the in­ teraction, is properly taken into account. Since the quark model can describe the short-range part of the N Nand Y N interactions within the unified framework of the resonating-group method (RGM). the symmetry properties of these interactions in the spin-flavor SU6 space become among the most important issues determining the quality of the model. A simultaneous description of the N Nand Y N interactions has recently been

Hierarchical wave function, Fock cyclic condition, and spin-statistics relation in the spin-singlet fractional quantum Hall effect.

We construct the hierarchical wave function of the spin-singlet fractional quantum Hall effect, which turns out to satisfy the Fock cyclic condition. The spin-statistics relation of the quasiparticles in the spin-singlet fractional quantum Hall effect is also discussed. Then we use particle-hole conjugation to check the wave function.

Particle-hole symmetry, F-spin, and r-process parameters.

We exploit approximate symmetry under particle-hole conjugation and the systematics associated with a classification scheme (inspired by the neutron-proton interacting boson model) to obtain estimates of binding energies and low-lying excitation energies for even-even r-process nuclei drawn from the major proton and neutron shells, 50Z82 and 82N126. We anticipate that our simple formalism for binding energies, depending on only six parameters, has an accuracy of \ensuremath{\sim}0.8 MeV. We argue that the particular dual particle-hole conjugation symmetry required to relate excitation energies in neutron-rich nuclei to the known excitation energies of the corresponding conjugated nuclei holds to within 10% or so.

Quasi-Kramers symmetries under particle-hole conjugation

The application of quasispin in nuclear, atomic and ligand field theory is extended here to systems of electron and hole states in a metallic systems. Conversely, results known in connection with particle-hole conjugation in metals are generalised to shell theoretic applications of quasispin. The analogy between the relationship of particle hole conjugation with quasispin and the relationship of time reversal with ordinary spin is extended to the development of selection rules parallelling those associated through Kramers with time reversal. Hamiltonians such as the BCS Hamiltonian which are composed of quasispin operators with real or imaginary coefficients have definite conjugation signature and so have a special interest. Several old and new results for matrix elements within a half-filled shell are derived from this viewpoint.

Spin‐free quantum chemistry. XIX. Particle‐hole and pairing symmetries

AbstractParticle–hole and pairing relationships are obtained within the framework of the unitary group formulation of the many‐electron problem using the concept of particle–hole conjugation. Besides the familiar relationships for alternant hydrocarbons, relationships among various pericyclic reaction paths are obtained.

Structure of 0 + states of 28Si and particle-hole conjugation

Full sd-shell calculations for the 0 + states of 28Si have been performed in the SU(3) basis so that the intrinsic deformation of the shell model states can be deduced by inspection. The shell model Hamiltonian is decomposed in a symmetric part H S and an antisymmetric part H A with respect to particle-hole conjugation. It is shown that the splitting of prolate and oblate states is due to the spin-orbit part of H A. The different prediction for 28Si obtained with Kuo and with Preedom-Wildenthal matrix elements can be attributed to the difference in a single parameter: the strength of the spin-orbit part of H A.

A realization of the particle-hole conjugation operator in the shell model

A quasi-spin representation of the particle-hole conjugation operator in one j-shell is given. Extension to the case of protons and neutrons allows a similar representation for the conjugation between a proton and a neutron hole. This is useful in the discussion of a symmetry property of systems self-conjugate under this conjugation.

Five-dimensional quasispin toward a complete classification of the isospin characteristics of shell-model states in the seniority scheme

A solution is proposed for the inner multiplicity problem associated with the five-dimensional quasispin description of shell-model states. A classification scheme, in terms of an orthonormal basis, leads to tractable results with definite symmetry properties under particle-hole conjugation. Explicit constructions are given for the R(5) irreducible representations (ω 1 1), (ω 1 3/2), (t + 1, t) for which the inner multiplicities are never greater than two. For states of seniority v = 2, reduced isospin t = 1, of a configuration j n general expressions are given for the matrix elements of an arbitrary two-body interaction, to determine their n, T dependence, and to isolate those features of the actual interaction among nucleons which are most effective in splitting the isospin degeneracy of such states.

Particle-hole conjugation in the shell model

The idea of particle-hole conjugation is expounded in the language of second quantization. Results of Racah are rederived and in particular a theorem important for the classification of half-filled shells.