Abstract:
In quantum spin systems obeying hyperscaling, the probability distribution of the total magnetization takes on a universal scaling form at criticality. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.

Abstract:
The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.

Abstract:
We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums respectively, we derive analytic expressions for the asymptotic behaviour of one and two point correlators. We discuss quenches within the ordered and disordered phases as well as quenches between the phases and to the quantum critical point. We give detailed account of both methods.

Abstract:
We develop a non-perturbative method to calculate the density of states (DOS) of the fluctuating gap model describing the low-energy physics of electrons on a disordered Peierls chain. For real order parameter field we calculate the DOS at the Fermi energy exactly as a functional of the disorder for a chain of finite length L. Averaging rho (0) with respect to a Gaussian probability distribution of the Peierls order parameter, we show that in the thermodynamic limit the average DOS at the Fermi energy diverges for any finite value of the correlation length above the Peierls transition. Pseudogap behavior emerges only if the Peierls order parameter is finite and sufficiently large.

Abstract:
We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as $\sqrt{\lambda}$ (and the dimerized bond order scales as $\lambda$) as $\lambda \to 0$ (where $\lambda$ is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at $\lambda=0$ in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions for the bond order follow the classical prediction as a function of inverse chain size for small $\lambda$. We therefore conclude that the zero $\lambda$ phase transition is of the mean-field type.

Abstract:
In order to reveal the relaxation mechanism of photogenerated charge-transfer excitations in quasi-one-dimensional halogen-bridged diplatinum complexes, we calculate the low-lying adiabatic potential energy surfaces of a one-dimensional extended Peierls-Hubbard model. High-energy excitations above the electron-hole continuum may relax into polarons, while excitons pumped within the optical gap are self-localized and then either decay by luminescence or divide into solitons. Neutral solitons, charged solitons, and polarons may be simultaneously photogenerated in a diplatinum-halide chain, which has never been observed in any conventional platinum-halide chain. Optical conductivity is also simulated along the decay paths for experimental verification.

Abstract:
The spin-Peierls instability in spin 1/2 XY chain coupled to dispersionless phonons of frequency $\omega$ has been studied in the nonadiabatic limit. We have chosen the Lang-Firsov variational wave function for the phonon subsystem to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then solved in the framework of mean-field approximation. We observed a dimerized phase when g is less than a critical value and an anti-ferromagnetic phase when it is greater than a critical value . The variation of lattice distortion, dimerized order parameter and energy gap with spin phonon coupling parameter has also been investigated here.

Abstract:
We extend previous analytical studies of the ground-state phase diagram of a one-dimensional Heisenberg spin chain coupled to optical phonons, which for increasing spin-lattice coupling undergoes a quantum phase transition from a gap-less to a gaped phase with finite lattice dimerisation. We check the analytical results against established four-block and new two-block density matrix renormalisation group (DMRG) calculations. Different finite-size scaling behaviour of the spin excitation gaps is found in the adiabatic and anti-adiabatic regimes.

Abstract:
The exact solution for the two particle spectrum of the Heisenberg-Peierls one dimensional spin chain is given by working in the fermionic representation. The resulting equations for the eigenvalues are, in some sense, similar to those of the Richardson's solution of the BCS model and must be solved numerically.

Abstract:
By using the Fermi-Bose transformation, the antiferromagnetic chain is mapped into the bosonic field, and the energy density of the ground state and the excite states of the model are given. The relationship between the energy density of the ground state and the strength of distortion of the model is obtained. The results show that there exists a spin-Peierls transition in the model. Finally, the numerical simulation is performed to verify the above theoretical prediction.