Dimerized Phase Research Articles

Manipulation of asymmetric dimer phases on Si(001) by low-temperature scanning tunneling microscopy

Manipulation of asymmetric dimer phases on Si(001) by low-temperature scanning tunneling microscopy

Mean-field theory of the spin-Peierls transition

We revisit the problem of the spin-Peierls instability in a one-dimensional spin-$\frac{1}{2}$ chain coupled to phonons. The phonons are treated within the mean-field approximation. We use bosonization techniques to describe the gapped spin chain and then use the thermodynamic Bethe ansatz to obtain quantitative results for the thermodynamics of the spin-Peierls system in a whole range of temperature. This allows us to predict the behavior of the specific heat and the magnetic susceptibility in the entire dimerized phase. We study the effect of small magnetic fields on the transition. Moreover, we obtain the parameters of the Landau-Ginzburg theory describing this continuous phase transition near the critical point.

Siloxane antiferroelectric liquid crystalline dimer exhibiting two field-free zero birefringent states

We studied the optical and electro-optical properties of a siloxane antiferroelectric liquid crystalline dimer exhibiting a large molecular tilt that reached a maximum value of 53°. When the molecular tilt angle in the antiferroelectric phase exceeded 45°, it was found that the field-free position of the slow vibration direction, which corresponds to the largest refractive index, flipped from a position along the smectic layer normal, to a position perpendicular to it. When the tilt angle became 45°, a zero birefringent state, which was theoretically predicted by de Meyere in 1996, was also found to occur twice in the antiferroelectric phase of the siloxane dimer.

Néel-dimer transition in an antiferromagnetic Heisenberg model and deconfinement of spinons at the critical point

Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic(AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\alpha$ for the exchange coupling which connects the N\'eel ($\alpha=0$) and the dimer ($\alpha=1$) states. We employ the $CP^1$ (the Schwinger boson) representation of the $s={1\over 2}$ spin operator and integrate out the half of the $CP^1$ variables at odd sites and we obtain a $CP^1$ nonlinear $\sigma$ model. The effective coupling constant is a function of $\alpha$ and at $\alpha=0$ the $CP^1$ model is in the ordered phase which corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of $\alpha_C$ as $\alpha$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the $CP^1$ model is in a Higgs phase and low-energy excitations are gapless spin wave. In the dimer phase, a confinement phase of the gauge theory is realized and low-energy excitations are $s=1$ magnons. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in 3 spatial dimensions, is realized and $s={1\over 2}$ spinons appear as low-energy excitations.

Quantum critical behavior of the one-dimensional ionic Hubbard model

We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give strong evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong coupling phase can only partly be understood in terms of the strong coupling behavior of the ordinary Hubbard model.

Phase Transition in a One-dimensional Extended Peierls–Hubbard Model with a Pulse of Oscillating Electric Field: III. Interference Caused by a Double Pulse

In order to study consequences of the differences between the ionic-to-neutral and neutral-to-ionic transitions in the one-dimensional extended Peierls–Hubbard model with alternating potentials for the TTF–CA complex, we introduce a double pulse of oscillating electric field in the time-dependent Schrödinger equation and vary the interval between the two pulses as well as their strengths. When the dimerized ionic phase is photoexcited, the interference effect is clearly observed owing to the coherence of charge density and lattice displacements. Namely, the two pulses constructively interfere with each other if the interval is a multiple of the period of the optical lattice vibration, while they destructively interfere if the interval is a half-odd integer times the period, in the processes toward the neutral phase. The interference is strong especially when the pulse is strong and short because the coherence is also strong. Meanwhile, when the neutral phase is photoexcited, the interference effect is almost invisible or weakly observed when the pulse is weak. The photoinduced lattice oscillations are incoherent due to random phases. The strength of the interference caused by a double pulse is a key quantity to distinguish the two transitions and to evaluate the coherence of charge density and lattice displacements.

Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet.

We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.

Real space renormalization group with effective interactions: applications to 2-D spin lattices

The Bloch’s theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The J 2/J 1 checkerboard lattice is studied and a location of the phase transition between the Neel phase and the dimer phase is proposed.

Correlation exponentKρof the one-dimensional Kondo lattice model

We present results for the correlation exponent K_rho of the Tomonaga-Luttinger liquid description of the one-dimensional Kondo lattice as a function of conduction electron density and coupling constant. It is obtained from the first derivative of the Fourier transform of the charge-charge correlation function. We also show that the spin correlation function can only be described in this picture if we include logarithmic corrections, a feature that had been previously overlooked. A consistent description of both charge and spin sectors is then obtained. Finally, we show evidence that the spin sector of the dimerized phase at quarter-filling is gapless.

Phase Transition in a One-dimensional Extended Peierls–Hubbard Model with a Pulse of Oscillating Electric Field: I. Threshold Behavior in Ionic-to-Neutral Transition

Photoinduced dynamics of charge density and lattice displacements is calculated by solving the time-dependent Schrödinger equation for a one-dimensional extended Peierls–Hubbard model with alternating potentials for the mixed-stack organic charge–transfer complex, TTF–CA. A pulse of oscillating electric field is incorporated into the Peierls phase of the transfer integral. The frequency, the amplitude, and the duration of the pulse are varied to study the nonlinear and cooperative character of the photoinduced transition. When the dimerized ionic phase is photoexcited, the threshold behavior is clearly observed by plotting the final ionicity as a function of the increment of the total energy. Above the threshold photoexcitation, the electronic state reaches the neutral one with equidistant molecules after the electric field is turned off. The transition is initiated by nucleation of a metastable neutral domain, for which an electric field with frequency below the linear absorption peak is more effective than that at the peak. When the pulse is strong and short, the charge transfer takes place on the same time scale with the disappearance of dimerization. As the pulse becomes weak and long, the dimerization-induced polarization is disordered to restore the inversion symmetry on average before the charge transfer takes place to bring the system neutral. Thus, a paraelectric ionic phase is transiently realized by a weak electric field. It is shown that infrared light also induces the ionic-to-neutral transition, which is characterized by the threshold behavior.

Sodium pyroxene NaTiSi2O6: possible haldane spin-1 chain system.

Using a density functional approach, we study the structural and magnetic properties of the pyrox-ene compound NaTiSi2O6. While all previous workers are taking that NaTiSi2O6 is a quasi-one-dimensional S=1/2 system, our theoretical results indicate that this is a Haldane S=1 chain compound below the phase transition at 210 K. A good agreement is obtained between the calculated and the measured Ti-Ti distances in the dimerized low temperature phase. We present a simple explanation of the flow of the unusual phase transition which is taking place in this compound.

Regularly alternating spin-1/2 anisotropic XY chains: the ground-state and thermodynamic properties.

Using the Jordan-Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain with periodically varying intersite interactions and/or on-site fields. We consider in detail the properties of the chains having a period of the transverse field modulation equal to 3. The regularly alternating transverse Ising chain exhibits several quantum phase transition points, where the number of transition points for a given period of alternation strongly depends on the specific set of the Hamiltonian parameters. The critical behavior in most cases is the same as for the uniform chain. However, for certain sets of the Hamiltonian parameters the critical behavior may be changed and weak singularities in the ground-state quantities appear. Due to the regular alternation of the Hamiltonian parameters the transverse Ising chain may exhibit plateaulike steps in the zero-temperature dependence of the transverse magnetization vs transverse field and many-peak temperature profiles of the specific heat. We compare the ground-state properties of regularly alternating transverse Ising and transverse XX chains and of regularly alternating quantum and classical chains. Making use of the corresponding unitary transformations we extend the elaborated approach to the study of thermodynamics of regularly alternating spin-1/2 anisotropic XY chains without field. We use the exact expression for the ground-state energy of such a chain of period 2 to discuss how the exchange interaction anisotropy destroys the spin-Peierls dimerized phase.

Calorimetric study of crystalline dimer and polymerized phases of fullerene C 60

By high precision dynamic calorimetry the temperature dependences of heat capacity C p 0= f( T) for dimer of C 60, orthorhombic and rhombohedral polymerized phases of fullerene C 60 were determined in the temperature range 300–650 K. Besides, endothermic transformations caused by the depolymerization of the polymerized (dimeric) phases of C 60 were studied and their standard thermodynamic characteristics a temperature interval, enthalpy, entropy and Gibbs function were analyzed. Based on the thermodynamic and oscillation spectroscopy data, it was established that the depolymerization proceeds completely and the products formed are a monomer fcc phase of C 60. From the data of the present work and the heat capacity values measured by us earlier in a low-temperature interval, the thermodynamic functions of the substances, viz. the heat capacity C p 0( T), enthalpy H 0( T)− H 0(0), entropy S 0( T)− S 0(0) and Gibbs function G 0( T)− H 0(0), were calculated over the range from T→0 to (380–490) K at standard pressure. The results were discussed taking into account literature data. A sequence of a relative thermodynamic stability at 298.15 K and atmosphere pressure of the crystalline polymerized C 60 phases was arranged.

Ordered phases of XXZ-symmetric spin-1/2 zigzag ladder

Using bosonization approach, we derive an effective low-energy theory for XXZ-symmetric spin-1/2 zigzag ladders and discuss its phase diagram by a variational approach. A spin nematic phase emerges in a wide part of the phase diagram, either critical or massive. Possible crossovers between the spontaneously dimerized and spin nematic phases are discussed, and the topological excitations in all phases identified.

Calorimetric study of crystalline dimer and polymerized phases of fullerene C60

By high precision dynamic calorimetry the temperature dependences of heat capacity C p 0 = f ( T ) for dimer of C 60 , orthorhombic and rhombohedral polymerized phases of fullerene C 60 were determined in the temperature range 300–650 K. Besides, endothermic transformations caused by the depolymerization of the polymerized (dimeric) phases of C 60 were studied and their standard thermodynamic characteristics a temperature interval, enthalpy, entropy and Gibbs function were analyzed. Based on the thermodynamic and oscillation spectroscopy data, it was established that the depolymerization proceeds completely and the products formed are a monomer fcc phase of C 60 . From the data of the present work and the heat capacity values measured by us earlier in a low-temperature interval, the thermodynamic functions of the substances, viz. the heat capacity C p 0 ( T ), enthalpy H 0 ( T )− H 0 (0), entropy S 0 ( T )− S 0 (0) and Gibbs function G 0 ( T )− H 0 (0), were calculated over the range from T →0 to (380–490) K at standard pressure. The results were discussed taking into account literature data. A sequence of a relative thermodynamic stability at 298.15 K and atmosphere pressure of the crystalline polymerized C 60 phases was arranged.

Ring exchange in low-dimensional spin systems

The isotropic S=12 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the cluster expansion technique, and by bosonization in the weak coupling limit. It is found that a sufficiently large amount of ring exchange leads to a second-order phase transition into a spontaneously dimerized phase. The shape of the phase boundary in the vicinity of the exactly known transition point is obtained. The relevance of ring exchange for materials with 2D CuO2 planes is discussed.

An RKKY-induced dimerized phase of the Kondo lattice model

We clarify the nature of the dimerized ground state found in the one-dimensional Kondo lattice model at quarter conduction electron filling. The conduction electrons mediate, through the RKKY mechanism, the long-range interactions among localized spins necessary to induce dimerization in that sub-system. On the other hand, the feedback of the local moments on the conduction electron fluid does not induce dimerization in the latter, whose spin sector remains gapless. The same feedback, however, is able to open a charge gap.

Hole Dynamics in the Orthogonal-Dimer Spin System

The dynamics of a doped hole in the orthogonal-dimer spin system is investigated systematically in one, two and three dimensions. By combining the bond-operator method with the self-consistent Born approximation, we argue that a dispersive quasi-particle state in the dimer phase is well defined even for quasi-two-dimensional systems. On the other hand, a doped hole in the plaquette-singlet phase hardly itinerates, forming an almost localized mode. We further clarify that although the quasi-particle weight in the dimer phase is decreased in the presence of the interchain coupling, it is not suppressed but even enhanced upon the introduction of the interlayer coupling.

Metastable phase of symmetric dimers on Si(001)

The reconstruction of the Si(001) surface is reexamined by using first-principles density-functional calculations. We find that a symmetric dimer structure in which symmetric dimers are alternately displaced up and down along the dimer rows is more favored by 21 meV/dimer than the conventional symmetric dimer structure where all the dimers have an identical height. In this metastable $p(2\ifmmode\times\else\texttimes\fi{}2)$ structure, the up and down symmetric dimers accompany the lateral movements of the second-layer atoms: i.e., on the two sides of the dimer the second-layer atoms bonding to the up (down) dimer move equally toward (outward) each other by 0.15 \AA{}. With this predicted symmetric dimer structure we discuss the symmetric dimer phase observed in a recent low-temperature scanning tunneling microscopy experiment.

Antiferromagnetic Heisenberg Chains with Bond Alternation and Quenched Disorder

We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We discuss consequences of our results for the experimentally measured low-temperature susceptibility of CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2.