Stellan Ostlund

Density-matrix renormalization group for a gapless system of free fermions

We investigate convergence of the density matrix renormalization group (DMRG) in the thermodynamic limit for gapless systems. Although the DMRG correlations always decay exponentially in the thermodynamic limit, the correlation length at the DMRG fixed-point scales as

Symmetries and mean-field phases of the extended Hubbard model

\xi \sim m^{1.3}

Circle maps with symmetry-breaking perturbations

, where

The Nobel Symposium 156 new forms of matter: topological insulators and superconductors

m

Thermodynamic limit of density matrix renormalization.

is the number of kept states, indicating the existence of algebraic order for the exact system. The single-particle excitation spectrum is calculated, using a Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the symmetry

CLASS OF ANSATZ WAVE FUNCTIONS FOR ONE-DIMENSIONAL SPIN SYSTEMS AND THEIR RELATION TO THE DENSITY MATRIX RENORMALIZATION GROUP

E(k)=E(\pi -k)

d-wave pairing in tetragonal superconductors.

for translationally invariant half-integer spin-systems with local interactions. Finally, we provide a method to compute overlaps between ground states obtained from different DMRG calculations.

Staggered flux and stripes in doped antiferromagnets

The two-dimensional extended Hubbard model that includes a nearest-neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations permitting both broken gauge, spin, and sublattice symmetry. The theory is further extended to incorporate a possible twist in the spin-quantization axis, so that the competition between superconductivity, charge density waves, and Neel and spiral antiferromagnetic order can be monitored within one single theory. Our results for positive Hubbard {ital U} and Heisenberg exchange {ital J} suggest that antiferromagnetic ordering dominates close to half-filling, while spiral states and {ital d}-wave superconductivity compete when doping is introduced. For moderate values of {ital J}, we find a phase diagram where a phase transition occurs from an antiferromagnet to a {ital d}-wave superconductor as doping is increased. A narrow region of ({ital s}+{ital id})-wave superconductor is found for some values of {ital J} and {ital U}.

Thermodynamic limit and matrix-product states

Abstract Renormalization group methods are used to describe the transition to chaos that occurs in dissipative quasiperiodic systems in the presence of a small subharmonic perturbation. This is accomplished by studying the circle map with the symmetry θ → θ + 2 π / n , and looking at crossover exponents for perturbations obeying the usual 2π symmetry. In order to interpret these exponents, the standard renormalization group analysis must be extended to include extra functions. This has been worked out in detail for the case n = 2.

Fictitious fluxes in the quantum antiferromagnet

Eddy Ardonne Hans Hansson and Stellan Ostlund 1 Stockholm University, Sweden Chalmers University of Technology, Sweden The Nobel Symposium 156, ‘New forms of matter: topological insulators and superconductors’ took place from Friday 13 June until Sunday 15 June 2014. The venue for this Symposium was Hogberga Gard, on Lindingo, an island just east of Stockholm. The aim of the Symposium was to bring together leading scientists to discuss the latest results and important future directions in the rapidly developing field of topological states of matter. The Symposium welcomed 52 international participants, and 22 local observers. The program of the Symposium consisted of six sessions, each of which was introduced by an introductory talk, followed by shorter presentations. The last ordinary session was followed by a lively panel discussion. In these Proceedings, you will find a selection of the topics that were discussed during the Symposium. We would like to thank Petra Nodler for her invaluable administrative support, as well as the Knut and Alice Wallenberg Foundation, the Nobel Foundation, Nordita and Stockholm University, who supported this Nobel Symposium.