Ferromagnetic ground states of the Hubbard model on a complete graph

We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings N. We find that for t > 0 and for N = f + 1 the ground state is maximally ferromagnetic with total spin S = (f ? 1)/2.For N > f + 1 the ground state is still ferromagnetic but becomes degenerate with respect to S.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Bistability transition in the self-trapping of an electron in a one-dimensional molecular chain

Semi-classical approach to study the self-trapping of an electron in a linear molecular chain of finite number of sites N reveals a bistability reflecting two degenerate ground state configurations of the electron-lattice system. This bistability emerges as a result of symmetry breaking which occurs only for even N when the electron-phonon coupling exceeds a threshold. As a result, bifurcation diagrams for site displacements are obtained.     

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on \({s\in [0,1]}\), such that for each s, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that ’belong to the same phase’ are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an s-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings’ ‘quasi-adiabatic evolution’ technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the spectral flow, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models H(s), 0 ≤ s ≤ 1.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

Baxter operators for arbitrary spin II

This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional s?₂ representations. We consider the Baxter operators used in Bazhanov et al. (1996, 1997, 1999, 2010) [1] and [2], formulate their construction uniformly with the construction of our previous paper. The building blocks of all global chain operators are derived from the general Yang-Baxter operators and all operator relations are derived from general Yang-Baxter relations. This leads naturally to the comparison of both constructions and allows to connect closely the treatment of the cases of infinite-dimensional representation of generic spin and finite-dimensional representations of integer or half-integer spin. We prove not only the relations between the operators but present also their explicit forms and expressions for their action on polynomials representing the quantum states.     

Degenerate ferrimagnetic ground state of frustrated kagome lattice

The frustrated Ising model on kagome lattice with nearest-neighboring antiferromagnetic interaction is investigated by using Monte Carlo simulation of the Wang-Landau algorithm and Glauber dynamics. The geometrical frustration leads to a particularly high degeneracy of ground states in this system. A small magnetic field applied can lift the degeneracy partially, and produce the magnetization plateau of 1/3 saturate value (Ms), which is analogous to the magnetic behavior in triangular antiferromagnetic system. However, different from the long-range ferrimagnetic state responsible for 1/3 Ms plateau in triangular lattice, the ferrimagnetic ground state corresponding to 1/3 Ms plateau in kagome lattice is short-ranged and still highly degenerate. Furthermore, the spin configuration of these degenerate ferrimagnetic ground states show an inherent characteristic that the spins along the magnetic field must be aligned on the closed loops, which can be well understood in terms of geometrical frustration.     

Magnetic properties of magnetoactive spin clusters

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([…] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter.     

Stark effect in diffused quantum wells

We study the longitudinal Stark effect in diffused AlGaAs/GaAs quantum wells grown along the [1,0,0] direction. The energies of the ground electron and hole states and the first excited hole state are calculated for different diffusion lengths and electric field strengths. The energies of the main optical transitions and their Stark shifts are found. The intensities of the transitions are considered in terms of the bound states spatial distributions. The calculations are carried out within the semi-empirical sp³s ^* tight-binding model including spin and the surface Green function matching method. We compare our results with those obtained by means of other theoretical methods.     

Spin interactions in a quantum ring containing a magnetic impurity

The exciton states in a CdTe semiconductor quantum ring containing a single magnetic impurity are considered in an external magnetic field. The electron-hole spin interaction and s,p-d interactions between electron, hole and magnetic impurity are also taken into account in the calculations. It is shown that due to the s,p-d spin interactions the ground state exciton energy splits into 12 doubly degenerated energy levels. The external magnetic field removes this degeneracy. A novel method is proposed here to determine the values of the strengths of s,p-d interactions. The optical spectrum of the system for different polarizations of the incident light and for different initial states of the magnetic impurity spin projection is also studied.     

The microwave spectrum of sodium tetrahydroborate NaBH4 in excited vibrational states: Coriolis interaction between the Na-BH4 stretching and the BH4 rocking vibrations

Two sets of vibrational satellites have been observed in the rotational spectrum of sodium tetrahydroborate NaBH₄, and have been assigned to the non-degenerate, Na—BH₄ stretching and the degenerate BH₄ rocking (or internal rotation) states. The observation was extended from the J = 11 ← 10 up to J = 20 ← 19 transitions. The vibrational satellites showed anomalous K structure; higher-K lines of the non-degenerate state appeared at higher frequencies, in reverse to those of the ground state, whereas the spectra in the degenerate state exhibited a K pattern similar to but somewhat more widely spread than that of the ground state. These anomalies are ascribed to the Coriolis interaction between the two excited vibrational states. The spectra observed were analysed using a C_3v symmetric-top rotational Hamiltonian, which took into account the Coriolis interaction explicitly. The A rotational constants, the energy difference δE between the two interacting vibrational states, and the first- and second-order Coriolis interaction constants have been derived.     

Green's functions for open-shell atoms and molecules

Green's functions for atoms and molecules with a degenerate ground state are evaluated by means of tensorial analysis. The final results obtained are of simple character allowing the usual diagrammatic approach via Wick's theorem for non-degenerate ground states. As an example the ionization of a σ orbital of O₂ is considered and an equivalent approach to the frozen orbital approximation is discussed.     

Entanglement and elementary excitations in quantum spin chain

The entanglement induced by elementary excitations in the XX spin chain is investigated by Bethe ansatz method. The reduced density matrix and correlation function between any pair of spins can be obtained for ground and all excited states with N qubits. Rely on them we show the explicit and general relations between entanglement and elementary excitations in XX spin chain. We further show our method can be extend to other integrable models.     

Spinor Structure and Matter Spectrum

Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations). All these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type (l, 0) ⊕ (0, l), where l is a spin value, whereas for arbitrary spin chains we have degenerate spectrum. Energy spectra of the stability levels (electron and proton states) of the matter spectrum are studied in detail. It is shown that these stability levels have a nature of threshold scales of the fractal structure associated with the system of interlocking representations of the Lorentz group.     

Combining spin-adapted open-shell TD-DFT with spin–orbit coupling

The recently proposed spin-adapted time-dependent density functional theory (S-TD-DFT) is extended to the relativistic domain for fine-structure splittings of excited states of open-shell systems. Scalar-relativistic effects are treated to infinite order via the spin-free (sf) part of the exact two-component (X2C) Hamiltonian, whereas the spin–orbit couplings (SOC) between the scalar-excited states are treated perturbatively via an effective one-electron spin–orbit operator derived from the same X2C Hamiltonian. The calculated results for prototypical open-shell systems containing heavy elements reveal that the composite approach sf-X2C-S-TD-DFT-SOC is very promising. The fine-structure splitting of a spatially degenerate ground state can also be described properly by taking a non-degenerate excited state as the reference.     

Reggeon field theory for α(0) > 1

We obtain the asymptotic behaviour of the scattering amplitude when the pomeron has intercept α(0) larger than one. The reggeon field theory is studied by introducing a lattice in impact parameter space. Use is made of a previous result showing asymptotically the dynamics is controlled at each lattice site (α′ = 0 case) by a two-level structure. This leads to a non-Hermitean Hamiltonian expressed in terms of spin operators in which the intersite interaction terms is proportional to the pomeron slope α′. The spectrum of such a system shows a degenerate ground state for α(0) > α_c >~ 1 and a continuum with vanishing excitation gap at α(0) = α_c. The vacuum does not change structure at the critical value. The critically is shown by an order parameter which is given by the matrix element of a field operator between the vacuum and its degenerate companion. The nature of this critical phenomenon is better understood by continuously transforming the Hamiltonian into that of an Ising model with a transverse field which shows a well-known second-order phase transition. By defining the S-matrix so as to preserve the formal perturbation expansion, we find that for α(0) > α_c, the zero gap state contributes a non-trivial asymptotic constant. The final asymptotic picture is that of a gray disc expanding like log s, so that the total cross section behaves as (log s)². For α(0) < α_C, the vacuum is non-degenerate and correspondingly the total cross section drops to zero as an inverse power of s.     

Effect of Nucleon Pairing in the Spectra of <Emphasis Type="Italic">N</Emphasis> = 50 Isotones

The emergence of the pairing effect of identical nucleons in the j = 9/2 state in low-lying excited states of nuclei near ⁹⁰Zr (N = 50, Z = 40) is discussed. Multiplets of states with seniority s ≥ 2, the splitting of which is determined by the proton pairing energy, are clearly visible in the nuclear spectra for a chain of N = 50 isotones. A comparison of the spectra of ground state multiplets, calculated in the δ-interaction approximation, with experimental data and results from other theoretical calculations shows this approach can be used to describe the structure of spectra and level positions with high J values.     

Broken symmetry in antiferromagnets

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.