Moderate deviations for the determinant of Wigner matrices

We establish a moderate deviations principle (MDP) for the log-determinant $\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.Comment: 20 pages, one missing reference added; Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics and Statistics, 201

Impurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method

We use the density matrix renormalization group (DMRG) for transfer matrices to numerically calculate impurity corrections to thermodynamic properties. The method is applied to two impurity models in the spin-1/2 chain, namely a weak link in the chain and an external impurity spin. The numerical analysis confirms the field theory calculations and gives new results for the crossover behavior.Comment: 9 pages in revtex format including 5 embedded figures (using epsf). To appear in PRB. The latest version in PDF format can be found at http://fy.chalmers.se/~eggert/papers/DMRGimp.pd

Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled $XY$-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

Thermodynamics of a one-dimensional S=1/2 spin-orbital model

The thermodynamic properties of a one-dimensional model describing spin dynamics in the presence of a twofold orbital degeneracy are studied numerically using the transfer-matrix renormalization group (TMRG). The model contains an integrable SU(4)-symmetric point and a gapless phase which is SU(4) invariant up to a rescaling of the velocities for spin and orbital degrees of freedom which allows detailed comparison of the numerical results with conformal field theory. We pay special attention to the correlation lengths which show an intriguing evolution with temperature. We find that the model shows an intrinsic tendency towards dimerization at finite temperature even if the ground state is not dimerized.Comment: 9 pages, 12 figure

On absolute moments of characteristic polynomials of a certain class of complex random matrices

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.Comment: 41 page, typos correcte

Interplay of quantum and thermal fluctuations in a frustrated magnet

We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the 3d XY universality class.Comment: 9 pages, revtex

Thermodynamic properties and thermal correlation lengths of a Hubbard model with bond-charge interaction

We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X using the transfer matrix renormalization group method (TMRG). Numerical results for various quantities like spin and charge susceptibilities, particle densities, specific heat and thermal correlation lengths are presented and discussed. We compare our data also to results for the exactly solvable case X/t=1 as well as to bosonisation results for weak coupling X/t << 1, which shows excellent agreement. We confirm the existence of a Tomonaga-Luttinger and a Luther-Emery liquid phase, in agreement with previous studies at zero temperature. Thermal singlet-pair correlation lengths are shown to dominate density and spin correlations for finite temperatures in certain parameter regimes.Comment: 13 pages, revte

Nonlinear excitations in CsNiF3 in magnetic fields perpendicular to the easy plane

Experimental and numerical studies of the magnetic field dependence of the specific heat and magnetization of single crystals of CsNiF3 have been performed at 2.4 K, 2.9 K, and 4.2 K in magnetic fields up to 9 T oriented perpendicular to the easy plane. The experimental results confirm the presence of the theoretically predicted double peak structure in the specific heat arising from the formation of nonlinear spin modes. The demagnetizing effects are found to be negligible, and the overall agreement between the data and numerical predictions is better than reported for the case when the magnetic field was oriented in the easy plane. Demagnetizing effects might play a role in generating the difference observed between theory and experiment in previous work analyzing the excess specific heat using the sine-Gordon model.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Staggered dimer order in S=1/2 quantum spin ladder system with four spin exchange

We study the S=1/2 quantum spin ladder system with the four-spin exchange, using density matrix renormalization group method and an exact diagonalization method. Recently, the phase transition in this system and its universality class are studied. But there remain controversies whether the phase transition is second order type or the other type and the nature of order parameter. There are arguments that the massless phase appears. But this does not agree with our previous result. Analyzing DMRG data, we try a new approach in order to determine a phase which appears after the phase transition. We find that the edge state appears in the open boundary condition, investigating excitation energies of states with higher magnetizations.Comment: Submitted to Phys. Rev. B, (REVTeX4