J. Sólyom

Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain

We study numerically the ground-state phase diagram of the bilinear-biquadratic spin-1 chain near the ferromagnetic instability point, where the existence of a gapped or gapless nondimerized quantum nematic phase has been suggested. Our results, obtained by a highly accurate density-matrix renormalization-group calculation, are consistent with the view that the order parameter characterizing the dimer phase vanishes only at the point where the system becomes ferromagnetic, although the existence of a gapped or gapless nondimerized phase in a very narrow parameter range between the ferromagnetic and the dimerized regimes cannot be ruled out.

String order in spin liquid phases of spin ladders

Two-leg spin ladders have a rich phase diagram if rung, diagonal and plaquette couplings are allowed for. Among the possible phases there are two Haldane-type spin liquid phases without local order parameter, which differ, however, in the topology of the short range valence bonds. We show that these phases can be distinguished numerically by two different string order parameters. We also point out that long range string- and dimer orders can coexist.

Entanglement patterns and generalized correlation functions in quantum many body systems

We define a generalized, entanglement-based correlation function related to the mutual information of two localized, typically single-site, subsystems of a larger many-body system. The two-site mutual information is defined in terms of the von Neumann entropy of the single-site and two-site density matrices, which, in turn, can be written in terms of expectation values of transition operators between localized states. It can be used to map out entanglement patterns between the subsystems, i.e., sites, of the system. Defining generalized correlation functions as two-point correlation functions of transition operators, we find that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. We show how the generalized correlation functions are related to conventional correlation functions for spin and fermion lattice models. We explore the behavior of the mutual information, the generalized correlation functions, and their relation for the general spin-1/2 Heisenberg model and for SU(n) Hubbard models with n = 2,3,4, and 5, demonstrating the principles on known phases of the spin and SU(2) Hubbard models and obtaining results characterizing the dimerized, trimerized, and quadrimerized phases in the SU(3), SU(4), and SU(5) Hubbard models, respectively. In addition, we extend the picture of the two-site mutual information and the corresponding generalized correlation functions to the n-site case.

Phase diagram of the t-U-J1-J2 chain at half filling

We investigate the half-filled Hubbard chain with additional nearest- and next-nearest-neighbor spin exchange, J1 and J2, using bosonization and the density-matrix renormalization group. For J2 = 0 we find a spin-density-wave phase for all positive values of the Hubbard interaction U and the Heisenberg exchange J1. A frustrating spin exchange J2 induces a bond-order-wave phase. For some values of J1, J2 and U, we observe a spin-gapped metallic Luther-Emery phase.

Stability of the Haldane phase in anisotropic magnetic ladders

We have considered the properties of anisotropic two-leg ladder models with S = 1/2 or S = 1 spins on the rungs, using Whites density matrix renor- malization group method. We have generalized the method by taking into account the symmetries of the model in order to reduce the dimensions of the matrix to be diagonalized, thereby making possible to consider more states. The boundaries in the parameter space of the extended region, where the Haldane phase exists, are estimated.

Dimerized phase in the cross-coupled antiferromagnetic spin ladder

We revisit the phase diagram of the frustrated s=1/2 spin ladder with antiferromagnetic rung and diagonal couplings. In particular, we reexamine the evidence for the columnar dimer phase, which has been predicted from analytic treatment of the model and has been claimed to be found in numerical calculations. By considering longer chains and by keeping more states than in previous work using the density-matrix renormalization group, we show that the numerical evidence presented previously for the existence of the dimerized phase is not unambiguous in view of the present more careful analysis. While we cannot completely rule out the possibility of a dimerized phase in the cross-coupled ladder, we do set limits on the maximum possible value of the dimer order parameter that are much smaller than those found previously.

Spatially nonuniform phases in the one-dimensional SU (n) Hubbard model for commensurate fillings

The one-dimensional repulsive SU

Mott transition and dimerization in the one-dimensional SU (n) Hubbard model

(n)

Periodic Anderson model with correlated conduction electrons: Variational and exact diagonalization study

Hubbard model is investigated analytically by bosonization approach and numerically using the density-matrix renormalization-group (DMRG) method for

Unified phase diagram of models exhibiting a neutral-ionic transition

n=3,4