Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9611057

A Modified Quantum Renormalization Group for xxz Spin Chain

A. Langari, Vahid Karimipour

Published Nov 6, 1996• 2 citations
arXivHTMLPDF

Abstract

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the xxz spin 1/2 Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin-spin correlation function which confirms the absence of long-range order in the massless region of the 1D xxz model.

DOI
10.48550/arxiv.cond-mat/9611057

Related papers

A Modified Quantum Renormalization Group for XXZ Spin Chain

A. Langari, Vahid Karimipour

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the XXZ spin-[Formula: see text] Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin–spin correlation function which confirms the absence of long-range order in the massless region of the 1D XXZ model.

International Journal of Modern Physics B•Sep 20, 1998•2 citations

Real Space Renormalization Group Study of the Long Range Order in the 2 Dimensional Spin 1/2XXZHeisenberg Model

Shu-ichi Nagasawa

The presence of the long range order in the ground state of the quantum XXZ Heisenberg model is investigated using real space renormalization group method. Our results suggest the existence of the long range order in the Z component of the spin for | J Z / J X |>1.0, and that in the XY component of the spin for | J Z / J X |<1.0.

Journal of the Physical Society of Japan•Jan 15, 1990•3 citations

Renormalization-group method for weakly coupled quantum chains: Application to the spin- 12 Heisenberg model

S. Moukouri

The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse couplings ${J}_{\ensuremath{\perp}}$ and ${J}_{d}$ (along the diagonals). An extensive comparison of the renormalization group and quantum Monte Carlo results for parameters where the simulations by the latter method are possible shows a very good agreement between the two methods. It is found, by analyzing ground state energies and spin-spin correlation functions, that there is a transition between two ordered magnetic states. When ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\lesssim}0.5$, the ground state displays a N\'eel order. When ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\gtrsim}0.5$, a collinear magnetic ground state in which interchain spin correlations are ferromagnetic becomes stable. In the vicinity of the transition point, ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\approx}0.5$, the ground state is disordered. But, the nature of this disordered ground state is unclear. While the numerical data seem to show that the chains are disconnected, the possibility of a genuine disordered two-dimensional state, hidden by finite size effects, cannot be excluded.

arXiv:cond-mat/0305608•Physical Review B•Jul 7, 2004•25 citations

Real-Space Renormalization Group (RSRG) Approach to Quantum Spin Lattice Systems

Alexander S. Serov, Геннадий Васильевич Коваль

The paper describes an explicit variational modification of the standard RSRG method and its application to quantum spin lattice systems. The modified approach is applied to exactly solvable ITF, XX and isotropic Heisenberg models. Better upper bounds for the systems' ground state energy are obtained as compared to the standard RSRG approach.

arXiv:1407.0041•Jun 30, 2014•0 citations

Correlation amplitude for the S=12 XXZ spin chain in the critical region: Numerical renormalization-group study of an open chain

Takashi Hikihara, Akira Furusaki

The density-matrix renormalization-group technique is used to calculate the spin-correlation functions $〈{S}_{j}^{x}{S}_{k}^{x}〉$ and $〈{S}_{j}^{z}{S}_{k}^{z}〉$ of the one-dimensional $S=\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.

arXiv:cond-mat/9803159•Physical review. B, Condensed matter•Jul 1, 1998•70 citations

Density-matrix renormalization-group analysis of the spin- 12 XXZ chain in anXYsymmetric random magnetic field

Laura Urba, Anders Rosengren

The spin-$\frac{1}{2} \mathrm{XXZ}$ chain in a random magnetic field pointing in the Z direction is numerically studied using the density-matrix renormalization-group method. The phase diagram as a function of the anisotropy of the $\mathrm{XXZ}$ Hamiltonian and the strength of the random field is analyzed by computing the spin correlations and the superfluid density. To obtain the superfluid density we consider a superblock configuration representing a closed system with an arbitrary twist at the boundary. This allows us to estimate the size of the critical region where the quasi-long-range order persists, that is, where the spin correlation length is infinite and the superfluid density is nonzero.

arXiv:cond-mat/0204539•Physical review. B, Condensed matter•Mar 14, 2003•11 citations
A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the xxz spin 1/2 Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin-spin correlation function which confirms the absence of long-range order in the massless region of the 1D xxz model.
A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the XXZ spin-[Formula: see text] Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin–spin correlation function which confirms the absence of long-range order in the massless region of the 1D XXZ model.
The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse couplings ${J}_{\ensuremath{\perp}}$ and Jd{J}_{d}Jd​ (along the diagonals). An extensive comparison of the renormalization group and quantum Monte Carlo results for parameters where the simulations by the latter method are possible shows a very good agreement between the two methods. It is found, by analyzing ground state energies and spin-spin correlation functions, that there is a transition between two ordered magnetic states. When ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\lesssim}0.5$, the ground state displays a N\'eel order. When ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\gtrsim}0.5$, a collinear magnetic ground state in which interchain spin correlations are ferromagnetic becomes stable. In the vicinity of the transition point, ${J}_{d}∕{J}_{\ensuremath{\perp}}\ensuremath{\approx}0.5$, the ground state is disordered. But, the nature of this disordered ground state is unclear. While the numerical data seem to show that the chains are disconnected, the possibility of a genuine disordered two-dimensional state, hidden by finite size effects, cannot be excluded.
The density-matrix renormalization-group technique is used to calculate the spin-correlation functions 〈SjxSkx〉〈{S}_{j}^{x}{S}_{k}^{x}〉〈Sjx​Skx​〉 and 〈SjzSkz〉〈{S}_{j}^{z}{S}_{k}^{z}〉〈Sjz​Skz​〉 of the one-dimensional S=12S=\frac{1}{2}S=21​ XXZ\mathrm{XXZ}XXZ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.
The spin-12XXZ\frac{1}{2} \mathrm{XXZ}21​XXZ chain in a random magnetic field pointing in the Z direction is numerically studied using the density-matrix renormalization-group method. The phase diagram as a function of the anisotropy of the XXZ\mathrm{XXZ}XXZ Hamiltonian and the strength of the random field is analyzed by computing the spin correlations and the superfluid density. To obtain the superfluid density we consider a superblock configuration representing a closed system with an arbitrary twist at the boundary. This allows us to estimate the size of the critical region where the quasi-long-range order persists, that is, where the spin correlation length is infinite and the superfluid density is nonzero.