Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9908200

Density Matrix Renormalisation Group Variants for Spin Systems

M. S. L. du Croo de Jongh
View original source ↗Read source document ↗Export metadata ↓

Abstract

This thesis gives an extension for the Density Matrix Renormalisation Group (DMRG) to two dimensions and described a newly developed combination of the DMRG and a Green Function Monte Carlo simulation (GFMC). The first two chapters focus on the DMRG method. The properties are reviewed and it is shown that good quality results can be obtained for two-dimensional systems through finite-size scaling. In the third and fourth chapter the properties of the two-dimensional frustrated Heisenberg model are analysed using a similar combination of DMRG and finite-size scaling. The final chapter presents the combination of the DMRG and GFMC with Stochastic Reconfiguration (Sorella, Capriotti cond-mat/9902211) We find an intermediate phase between Neel and collinear long-range order. This phase shows spatial inhomogeneities with a tendency towards plaquette formation.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. S. L. du Croo de Jongh. 1999-08-13. Density Matrix Renormalisation Group Variants for Spin Systems. https://arxiv.org/abs/cond-mat/9908200

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification using X-rays and binary alloys appears well within the existing techniques, while feasibility for neutron scattering requires further study. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

cond-mat.stat-mech↗
arXiv2026

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble

We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form $ω^{2}=k^{2}+4E_{*}^{-1/2}k^{5/2}$, where $E_{*}$ sets the characteristic scale of the multifractional correction. Working within the grand-canonical ensemble, we derive the modified density of states, the grand potential, the partition function, and the main thermodynamic quantities for both bosonic and fermionic sectors. The deformation changes the available phase-space distribution and produces nonstandard thermal scalings controlled by the ratio $T/E_{*}$. In the infrared regime, the usual relativistic gas behavior is recovered with leading corrections proportional to powers of $(T/E_{*})^{1/2}$. In the ultraviolet regime, the density of states scales as $\varrho(ω)\propto ω^{7/5}$, corresponding to an effective density-of-states dimension $d_{\mathrm{eff}}=12/5$. As a consequence, the Stefan-Boltzmann law is deformed from $u\propto T^{4}$ to $u\propto E_{*}^{3/5}T^{17/5}$, while the equation-of-state parameter approaches $w=5/12$ instead of the standard radiation value $w=1/3$. We also analyze thermal stability, particle number and energy fluctuations, Bose-Einstein condensation, and the degenerate Fermi gas limit. The multifractional correction increases the critical temperature of a conserved bosonic gas and modifies the Fermi energy, pressure, sound speed, and low-temperature heat capacity of degenerate fermions. A direct fit to the COBE/FIRAS monopole spectrum yields $E_{*}>0.36\,\mathrm{MeV}$ at $95\%$ CL, while the conservative GWTC--3 propagation constraint gives $E_{*}>1.18\times10^{19}\,\mathrm{GeV}$ at $90\%$ credibility when the dispersion relation is assumed to be universal.

cond-mat.stat-mech↗
arXiv2026

Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory

We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.

cond-mat.stat-mech↗