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

Physical Review Letters

Monte Carlo Renormalization Group for Quantum Systems

M. Kolb

Published Oct 31, 1983• 15 citations
Publisher

Abstract

A real-space renormalization-group transformation for quantum systems is proposed, based on an equivalent classical representation. Classical real-space renormalization groups and in particular Monte Carlo renormalization groups can then be used to study quantum systems. This formulation is valid for zero temperature as well as finite temperature. The Ising model in a transverse field in one and two dimensions is treated by Monte Carlo renormalization group.

DOI
10.1103/physrevlett.51.1696

Related papers

Monte Carlo renormalization group for quantum systems

M. A. Novotny, David Paul Landau

A Monte Carlo renormalization-group (MCRG) method developed to study quantum systems is presented. This MCRG method is the synthesis of the Monte Carlo method for quantum systems using the Trotter transformation with the MCRG developed for classical systems. It is applicable to the study of either the ground-state or the finite-temperature behavior of a quantum system. The convergence properties of this MCRG are illustrated by applying it to the ground state of the d=1 Ising model in a transverse magnetic field. Very rapid convergence to the known critical exponents is exhibited even for small lattice sizes.

Physical review. B, Condensed matter•Feb 1, 1985•9 citations

Zero-temperature renormalization method for quantum systems. I. Ising model in a transverse field in one dimension

Rémi Jullien, Pierre M. Pfeuty, J. N. Fields +1 more

A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical "magnetic" exponents near the transition.

Physical review. B, Condensed matter•Oct 1, 1978•143 citations

Renormalization-group transformation for quantum lattice systems at zero temperature

J. E. Hirsch, Gene F. Mazenko

We propose a new renormalization-group (RG) method applicable to quantum systems defined on a lattice at zero temperature. We apply our method to the one-dimensional Ising model in a transverse field and the two-dimensional triangular Ising model in a transverse field. In both cases, a nontrivial fixed point of our RG transformation is found. Critical exponents are calculated and compared with exact and previous RG results.

Physical review. B, Condensed matter•Mar 1, 1979•51 citations

Monte Carlo renormalization-group study of Ising spin glasses

Jian‐Sheng Wang, Robert H. Swendsen

We present a new Monte Carlo renormalization-group approach to spin glasses. Application of this approach to the \ifmmode\pm\else\textpm\fi{}J Ising spin glass shows clear differences between two-, three-, and four-dimensional models. The data are consistent with a zero-temperature transition in two dimensions, and finite-temperature transitions in three and four dimensions.

Physical review. B, Condensed matter•May 1, 1988•34 citations

Block-spin renormalization group in the large- n limit

J. E. Hirsch, Stephen H. Shenker

We present a real-space renormalization-group (RG) study of the $n$-component classical Heisenberg model in the large-$n$ limit. We obtain exact expressions for correlation functions of block spins, given those of the original spins. We show how to extract the critical behavior of the model from such information. The model provides a good testing ground for evaluating the effectiveness of Monte Carlo RG techniques. We study numerically the implementation of the real-space RG transformation on finite lattices. In two dimensions, we obtain the $\ensuremath{\beta}$ function as a function of temperature. In three dimensions, we calculate the critical temperature and the thermal exponent. We discuss the effects of the use of finite lattices and of the use of different forms for the initial action on the accuracy of the results.

Physical review. B, Condensed matter•Feb 1, 1983•36 citations

Monte Carlo Renormalization-Group Transformations in Momentum Space

Robert H. Swendsen

Methods of extending Monte Carlo renormalization-group calculations to include transformations in momentum space are proposed to investigate systems for which block spins are difficult or impossible to construct---such systems include fluids, for which particles are not confined to a lattice, three-dimensional fcc antiferromagnets, and lattice gauge models in four dimensions. The feasibility of these transformations is demonstrated by calculations in two and three dimensions.

Physical Review Letters•Oct 19, 1981•13 citations
A real-space renormalization-group transformation for quantum systems is proposed, based on an equivalent classical representation. Classical real-space renormalization groups and in particular Monte Carlo renormalization groups can then be used to study quantum systems. This formulation is valid for zero temperature as well as finite temperature. The Ising model in a transverse field in one and two dimensions is treated by Monte Carlo renormalization group.
A Monte Carlo renormalization-group (MCRG) method developed to study quantum systems is presented. This MCRG method is the synthesis of the Monte Carlo method for quantum systems using the Trotter transformation with the MCRG developed for classical systems. It is applicable to the study of either the ground-state or the finite-temperature behavior of a quantum system. The convergence properties of this MCRG are illustrated by applying it to the ground state of the d=1 Ising model in a transverse magnetic field. Very rapid convergence to the known critical exponents is exhibited even for small lattice sizes.
A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical "magnetic" exponents near the transition.
We present a real-space renormalization-group (RG) study of the nnn-component classical Heisenberg model in the large-nnn limit. We obtain exact expressions for correlation functions of block spins, given those of the original spins. We show how to extract the critical behavior of the model from such information. The model provides a good testing ground for evaluating the effectiveness of Monte Carlo RG techniques. We study numerically the implementation of the real-space RG transformation on finite lattices. In two dimensions, we obtain the $\ensuremath{\beta}$ function as a function of temperature. In three dimensions, we calculate the critical temperature and the thermal exponent. We discuss the effects of the use of finite lattices and of the use of different forms for the initial action on the accuracy of the results.