Dimerized Ground State Research Articles

Magnetism of hole-dopedCuO2spin chains inSr14Cu24O41: Experimental and numerical results

We study the magnetism of the hole-doped $\mathrm{Cu}{\mathrm{O}}_{2}$ spin chains in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ by measuring the Electron Spin Resonance (ESR) and the static magnetization $M$ in applied magnetic fields up to $14\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. In this compound, the dimerized ground state and the charge order in the chains are well established. Our experimental data suggest that at low temperatures the Curie-like increase of $M$ as well as the occurrence of the related ESR signal are due to a small amount of paramagnetic centers that are not extrinsic defects but rather unpaired Cu spins in the chain. These observations qualitatively confirm recent ab initio calculations of the ground state properties of the $\mathrm{Cu}{\mathrm{O}}_{2}$ chains in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Our complementary quantum statistical simulations yield that the temperature and field dependence of the magnetization can be well described by an effective Heisenberg model in which the ground state configuration is composed of spin dimers, trimers, and monomers.

Ground state properties of spin-Peierls ladder model with interchain superexchange interactions

The ground-state properties of spin-Peierls ladder model with interchain Heisenberg interaction and interchain Dzyaloshinskii-Moriya(DM)interaction are studied by Lanczos numerical method. We mainly concentrate on the influence of interchain Heisenberg interaction and interchain DM interaction on system dimerization. The results show that these two interchain interations always act against the dimerization of the system, and they can make system ground state dimerization diminishing, which means that increasing the system dimensions may reduce system dimerization, even destroy the dimerization phase.

Electronic and structural instabilities of mixed-stack organic charge-transfer salts

Electronic (valence) and structural (Peierls) instabilities occur either separately or together in organic charge-transfer (CT) crystals with mixed stacks of donors (D) and acceptors (A). A Peierls–Hubbard model, H CT, with site D, A energies and linear electron–phonon coupling in a harmonic lattice is shown to provide a unified microscopic description and to distinguish between thermal and quantum Peierls transitions. Vibrational, magnetic and structural data are interpreted as thermal Peierls transitions in two ionic CT salts and as dimerized ground states with spin solitons in other salts. Quantum Peierls transitions are identified in largely neutral salts, and a neutral–ionic crossover is discussed in a salt with dipolar disorder that suppresses the Peierls instability. The coincident Peierls and neutral–ionic transition of tetrathiafulvalene-chloranil (TTF-CA) is another special case of H CT.

Spin solitons in organic charge-transfer salts

Organic charge-transfer (CT) salts that crystallize in face-to-face stacks of π-electron donors (D) and acceptors (A) are one-dimensional electronic systems with strong coupling to lattice and molecular vibrations. Peierls–Hubbard models of CT salts resemble π-electron theory of conjugated polymers, although transfer integrals t along mixed DA stacks are considerably smaller. Strong D and A yield Peierls systems with dimerized ground states of ion radicals, D + and A −. Topological spin solitons separate regions of opposite dimerization, similarly to solitons in trans-polyacetylene, but are thermally accessible in ionic CT salts due to small t. Salts with still smaller t have Peierls transitions at T P < 300 K to undimerized stacks. A Peierls–Hubbard model, H CT, describes both types of salts and estimates of t are consistent with T P < 300 K in some salts and spin solitons in others with higher T P. Electron paramagnetic resonance (epr) spectra of single crystals provide direct evidence for spin solitons and one-dimensional electronic states. Spin solitons and H CT resolve longstanding conflicts between vibrational and magnetic data that indicate dimerized stacks in several prototypical CT salts, while structural data point to undimerized stacks with large thermal ellipsoids. The low energy scale, availability of single crystals and diversity of CT salts offer opportunities for detailed modeling.

Crystal symmetry and high-magnetic-field specific heat ofSrCu2(BO3)2

We report measurements of the specific heat of the quantum spin liquid system SrCu2(BO3)2 in continuous magnetic fields H of up to 33 T. The specific heat vs temperature at zero field shows an anomaly at 8 K, marking the opening of a gap in the spin singlet excitations. At fields H~12 T, we clearly see a second anomaly that shifts to lower temperatures as H is increased. We attribute its origin to single triplet excitations of the singlet dimer ground state. This conclusion is supported by calculations of the specific heat, which reproduce the experimental data, made using the finite temperature Lanczos method to solve a Shastry-Sutherland Hamiltonian including nearest and next-nearest neighbor Dzyaloshinsky-Moriya interactions. The parameters used to fit the data are the exchange constants J = 74 K and J'/J = 0.62, and the Dzyaloshinsky-Moriya coupling constants |D|=6.1K, and $|D'|=2.2K.

Spin systems with dimerized ground states

In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be completely characterized, it was only possible to provide necessary or sufficient conditions for the quantum case. First, for all DGS systems the interaction between the dimers must be balanced in a certain sense. Moreover, one can identify four special classes of DGS systems: (i) Uniform pyramids, (ii) systems close to isolated dimer systems, (iii) classical DGS systems, and (iv), in the case of $s=1/2$, systems of two dimers satisfying four inequalities. Geometrically, the set of all DGS systems may be visualized as a convex cone in the linear space of all exchange constants. Hence one can generate new examples of DGS systems by positive linear combinations of examples from the above four classes.

Nonadiabatical approach to the Dzyaloshinsky-Moriya interaction in theXYspin chain coupled with quantum phonons

Using the model of the DM interaction in $XY$ antiferromagnetic spin chain with spin-phonon coupling, the nonadiabatic effects on the DM interaction have been studied by developing a nonadiabatic analytical approach. The results show that in the nonadiabatic case, to a certain finite phonon frequency, there exists a finite critical value of spin-phonon coupling. As the spin-phonon coupling decreases to the critical value, the system becomes gapless and the spin dimerization is destroyed. The DM interaction leads the system to have a finite critical value of spin-phonon coupling even in the adiabatic limit. The increase in staggered DM interaction will decrease the critical value of spin-phonon coupling, but increase that of phonon frequency, therefore, favors the dimerization. The nonadiabaticity plays an important role in suppressing the enhancement effects of the DM interaction to the dimerization. The dimerized ground state when DM interaction is present can be destroyed by the quantum lattice fluctuations. The threshold value of $\ensuremath{\beta}$ changing the effect of the DM interaction on the dimerization from suppression to promotion is not simply a constant but a crossover. For appropriate fixed values of spin-phonon coupling, phonon frequency and $\ensuremath{\beta}$, as $D$ increases, the system undergoes a reentry of phase between spin-dimer state and gapless state.

Giant phonon softening in the pseudogap phase of the quantum spin systemTiOCl

We report infrared and Raman spectroscopy results of the spin-1/2 quantum magnet TiOCl. Giant anomalies are found in the temperature dependence of the phonon spectrum, which hint to unusual coupling of the electronic degrees of freedom to the lattice. These anomalies develop over a broad temperature interval, suggesting the presence of an extended fluctuation regime. This defines a pseudo-gap phase, characterized by a local spin-gap. Below 100 K a dimensionality cross-over leads to a dimerized ground state with a global spin-gap of about 2$\Delta_{spin}\approx$~430 K.

Spin-Liquid versus Dimerized Ground States in a Frustrated Heisenberg Antiferromagnet

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.

Magnetic-field-induced condensation of triplons in Han Purple pigment BaCuSi2O6.

Besides being an ancient pigment, BaCuSi2O6 is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap, creating a gas of bosonic spin triplet excitations. The topology of the spin lattice makes BaCuSi2O6 an ideal candidate for studying the Bose-Einstein condensation of triplet excitations as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid helium temperatures.

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.

Density matrix renormalization calculations of the relaxed energies and solitonic structures of polydiacetylene

The density matrix renormalization group method is applied to the Pariser-Parr-Pople-Peierls model to calculate the energies and associated structures of the low-lying states of polydiacetylene. The extrinsic dimerization of polydiacetylene, arising from the electrons in ${p}_{y}$ orbitals in the triple bonds, is explicitly calculated. We find the following results. (i) Electronic interactions result in a twofold increase in the ground state dimerization, and a twofold decrease in the electronic correlation length, $\ensuremath{\xi}.$ (ii) The vertical energy of the ${2}^{1}{A}_{g}^{+}$ state lies circa. 1 eV above the ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state in long chains. (iii) The ${1}^{3}{B}_{u}^{+}$ and ${2}^{1}{A}_{g}^{+}$ states undergo a sizable electron-lattice relaxation, while this is modest for the ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state. As a consequence, the relaxed energy of the ${2}^{1}{A}_{g}^{+}$ lies circa 0.1 eV below the relaxed energy of the ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state. (iv) The reduction in $\ensuremath{\xi}$ results in a reversal in bond dimerizations in both the ${1}^{3}{B}_{u}^{+}$ and ${2}^{1}{A}_{g}^{+}$ states (in contrast to the noninteracting Peierls model). However, the excitonic ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state shows a polaronic distortion. We compare our results to experiment. For short oligomers the comparisons are very reasonable, but they are less satisfactory for long chains. The inclusion of solvation effects and a reparametrization of the Ohno interaction may both be necessary.

Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3

Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

Ground state and excitation of an asymmetric spin ladder model

We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange ${J}_{1}$ and different exchange integrals ${J}_{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing ${J}_{2}{=J}_{1}/2,$ we find, as a function of $\ensuremath{\delta},$ a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange $\ensuremath{\delta},$ the gap size of excitations is found to decrease with increasing $\ensuremath{\delta}.$ We also extend our study to a two-dimensional double layer model with an exactly known ground state.

The extended spin ladder and net models: exact dimer ground state and quantum phase transition

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Butterfly hysteresis and slow relaxation of the magnetization in (Et 4N) 3Fe 2F 9: manifestations of a single-molecule magnet

(Et 4N) 3Fe 2F 9 exhibits a butterfly-shaped hysteresis below 5 K when the magnetic field is parallel to the threefold axis, in accordance with a very slow magnetization relaxation in the timescale of minutes. This is attributed to an energy barrier Δ=2.40 K resulting from the S=5 dimer ground state of [Fe 2F 9] 3− and a negative axial anisotropy. The relaxation partly occurs via thermally assisted quantum tunneling. These features of a single-molecule magnet are observable at temperatures comparable to the barrier height, due to an extremely inefficient energy exchange between the spin system and the phonons. The butterfly shape of the hysteresis arises from a phonon avalanche effect.

A study of Peierls instabilities for a two-dimensional t-t' model

In this paper we study Peierls instabilities for a half-filled two-dimensional tight-binding model with nearest-neighbour hopping $t$ and next nearest-neighbour hopping $t'$ at zero and finite temperatures. Two dimerization patterns corresponding to the same phonon vector $(\pi, \pi)$ are considered to be realizations of Peierls states. The effect of imperfect nesting introduced by $t'$ on the Peierls instability, the properties of the dimerized ground state, as well as the competition between two dimerized states for each $t'$ and temperature $T$, are investigated. It is found: (i). The Peierls instability will be frustrated by $t'$ for each of the dimerized states. The Peierls transition itself, as well as its suppression by $t'$, may be of second- or first-order. (ii). When the two dimerized states are considered jointly, one of them will dominate the other depending on parameters $t'$ and $T$. Two successive Peierls transitions, that is, the system passing from the uniform state to one dimerized state and then to the other take place with decrease of temperature for some $t'$ values. Implications of our results to real materials are discussed.

Elementary Excitation and Ground-State Properties of Dimerized XXZ Chain with Frustration

We employ bosonization technique and quantum self-consistent theory to study the elementary excitation and ground-state properties of a dimerized XXZ S = 1/2 antiferromagnetic chain with frustration. The ground-state energy and one-magnon excited energy gap are calculated for frustration a > α c (γ), where a = α c (γ) is a critical line of frustration as a function of anisotropy on which there is a transition into a spontaneously dimerized ground state. It is shown that the ground-state energy decreases and the excited energy gap increases with increasing either frustration or dimerization for an anisotropic chain. We find that the dimerization dependence of the ground-state energy for small dimerization obeys the power law only on a = α c (γ), whereas it becomes a linear law when frustration and anisotropy parameters are far away from the critical line in the gapful range. The behavior of spin correlation in the ground state is also discussed analytically, which decays exponentially indicating a singlet ground state with an excited gap.

Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed.