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. B, Condensed matter

Equivalence of real-space renormalization groups for quantum systems and for critical dynamics

T. Schneider, Marco Zannetti

Published Nov 1, 1985• 4 citations
Publisher

Abstract

We demonstrate the equivalence of the real-space renormalization group for critical dynamics, and of the real-space renormalization group for quantum systems through the mapping of the master equation onto an imaginary-time Schr"odinger equation, defining the quantum system.
DOI
10.1103/physrevb.32.6108

Related papers

Real-space dynamic renormalization group. I. General formalism

Gene F. Mazenko, Michael J. Nolan, Oriol T. Valls

A general scheme is presented for applying real-space renormalization-group methods to dynamic critical phenomena. The method is based on mapping the time evolution operator for the initial variables onto a new operator acting on the block variables. The general formalism is discussed in the context of the kinetic Ising model. It is shown that all non-Markovian effects in the new operator can be eliminated if the renormalization-group transformation is taken to be the solution of a generalized eigenvalue equation. We show how to solve this equation perturbatively. The resulting transformation is such that the dynamics of the block spins is given by the slowest dynamic modes of the initial spins within a block.

Physical review. B, Condensed matter•Aug 1, 1980•26 citations

Real-Space Renormalization Group for Critical Dynamics

Y Achiam, J. Michael Kosterlitz

We propose a real-space renormalization-group technique to treat dynamic critical phenomena in two-dimensional Glauber-Ising models. The invariant form of the time-dependent probability distribution is found within linear response theory and an estimate of the dynamic exponent $z$ is given.

Physical Review Letters•Jul 10, 1978•73 citations

The Transition Point Between Classical and Quantum Mechanical Systems Deterministically Defined

Terence William Barrett

From a deterministic point of view of quantum theory the Schrodinger equation, considered as an equation of motion, is defined within an area of instability formed by two potential minima.This view can be related to the renormalization group theory of critical phenomena, and the location of two nontrivial fixed points can be defined with respect to those two potential minima.The renormalization group theory parameter: d, the dimensionality of space, defines the transition between classical and quantum theory.For a system in which d 2 4, classical mechanics applies, and for d < 4, quantum mechanics applies.Whereas the classical potential defining an equation of motion has one potential minimum (at the Gaussian fixed point), the quantum potential defining an equation of motion has two potential minima (at the nontrivial fixed points).An analogy exists between systems based on wave mechanics and those based on lattice systems.The underlying dynamics of that potential, the minimization of which results in an equation formally equivalent to the Schrodinger equation, can, in this formal analogy, be identified with the underlying dynamics of the exchange energy at the vertex of a lattice.There is thus a mathematical global similarity underlying the behavior of these two distinct theoretical frameworks which describes both.The principal and angular momentum quantum numbers of electron systems in this analogy are equivalent to the dimensionality of space, d, and the dimensionality of spin space, n, in the general theory of critical phenomena.The general theory describes the phase transitions of electron (wave mechanical) systems, and also a "Mendeleev's table" based on the d and n parameters constructed for those electron systems, in analogy with such a table for lattice systems.

Physica Scripta•Apr 1, 1987•1 citation

Monte Carlo Renormalization Group for Quantum Systems

M. Kolb

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.

Physical Review Letters•Oct 31, 1983•15 citations

Application of the Real-Space Renormalization Group to Dynamic Critical Phenomena

Gene F. Mazenko, Michael J. Nolan, Oriol T. Valls

We present a general approach for applying real-space renormalization-group methods to dynamic critical phenomena. In particular, we discuss the two-dimensional kinetic Ising model treating the interaction between blocks of spins as a small parameter.

Physical Review Letters•Aug 14, 1978•44 citations

Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms

Glen Evenbly, Guifré Vidal

The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D =1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.

arXiv:0801.2449•New Journal of Physics•Feb 26, 2010•49 citations
A general scheme is presented for applying real-space renormalization-group methods to dynamic critical phenomena. The method is based on mapping the time evolution operator for the initial variables onto a new operator acting on the block variables. The general formalism is discussed in the context of the kinetic Ising model. It is shown that all non-Markovian effects in the new operator can be eliminated if the renormalization-group transformation is taken to be the solution of a generalized eigenvalue equation. We show how to solve this equation perturbatively. The resulting transformation is such that the dynamics of the block spins is given by the slowest dynamic modes of the initial spins within a block.
We propose a real-space renormalization-group technique to treat dynamic critical phenomena in two-dimensional Glauber-Ising models. The invariant form of the time-dependent probability distribution is found within linear response theory and an estimate of the dynamic exponent zzz is given.
From a deterministic point of view of quantum theory the Schrodinger equation, considered as an equation of motion, is defined within an area of instability formed by two potential minima.This view can be related to the renormalization group theory of critical phenomena, and the location of two nontrivial fixed points can be defined with respect to those two potential minima.The renormalization group theory parameter: d, the dimensionality of space, defines the transition between classical and quantum theory.For a system in which d 2 4, classical mechanics applies, and for d < 4, quantum mechanics applies.Whereas the classical potential defining an equation of motion has one potential minimum (at the Gaussian fixed point), the quantum potential defining an equation of motion has two potential minima (at the nontrivial fixed points).An analogy exists between systems based on wave mechanics and those based on lattice systems.The underlying dynamics of that potential, the minimization of which results in an equation formally equivalent to the Schrodinger equation, can, in this formal analogy, be identified with the underlying dynamics of the exchange energy at the vertex of a lattice.There is thus a mathematical global similarity underlying the behavior of these two distinct theoretical frameworks which describes both.The principal and angular momentum quantum numbers of electron systems in this analogy are equivalent to the dimensionality of space, d, and the dimensionality of spin space, n, in the general theory of critical phenomena.The general theory describes the phase transitions of electron (wave mechanical) systems, and also a "Mendeleev's table" based on the d and n parameters constructed for those electron systems, in analogy with such a table for lattice systems.
The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D =1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.