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:quant-ph/0405168

Rethinking Renormalization for Quantum Phase Transitions

Hilary A. Carteret

Published May 28, 2004• 2 citations
arXivHTMLPDF

Abstract

This is a conceptual paper that re-examines the principles underlying the application of renormalization theory to quantum phase transitions in the light of quantum information theory. We start by describing the intuitive argument known as the Kadanoff ``block-spin'' construction for spins fixed on a lattice and then outline some subsequent ideas by Wilson and White. We then reconstruct these concepts for quantum phase transitions from first principles. This new perspective offers some very natural explanations for some features of renormalization theory that had previously seemed rather mysterious, even contrived. It also offers some suggestions as to how we might modify renormalization methods to make them more successful. We then discuss some possible order parameters and a class of functionals that are analogues of the correlation length in such systems.

DOI
10.48550/arxiv.quant-ph/0405168

Related papers

Renormalization Group: From a general concept to numbers

Jean Zinn‐Justin

Abstract Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

•Jun 19, 2019•0 citations

Scaling theories and the renormalization group

James H. Luscombe

The primary goal of modern theories of critical phenomena is the evaluation of critical exponents from first principles, implying the need to get beyond mean field theories which predict the same exponents independent of the nature of the system. This chapter focuses on a new approach emerged in the 1960s based on two ideas—scaling and renormalization. It presents the physical picture developed by L. P. Kadanoff that provides a conceptual basis for scaling and which has become part of the standard language of critical phenomena. Renormalization provides a way to calculate the free energy not involving a direct evaluation of the partition function—it's a new paradigm in statistical mechanics. The chapter analyzes a simplified, approximate set of recursion relations valid at high temperature for a model with nearest and next-nearest-neighbor interactions. In 1971 K. G. Wilson published two articles marking the introduction of the renormalization group to the study of critical phenomena.

CRC Press eBooks•Jan 9, 2021•0 citations

Relating Theories via Renormalization

Leo P. Kadanoff

The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of one hundred and fifty years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behavior separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications are summarized.

arXiv:1102.3705•Feb 17, 2011•5 citations

Some basic aspects of quantum phase transitions

D. V. Shopova, Dimo I. Uzunov

Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of quenched disorder on the quantum phase transitions is also discussed. The review is performed within the framework of the thermodynamic scaling theory and by the most general methods of statistical physics for the treatment of phase transitions: general lengthscale arguments, exact solutions, mean field approximation, Hubbard-Stratonovich transformation, Feynman path integral approach, and renormalization group in the field theoretical variant. Some new ideas and results are presented. Outstanding theoretical problems are mentioned. 1.

•Jan 1, 2003•23 citations

From quantum cognition to conceptuality interpretation II: unravelling the quantum mysteries

Diederik Aerts, Massimiliano Sassoli de Bianchi, Sandro Sozzo

An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies Heisenberg's uncertainty principle, wave function-based and entanglement-based non-locality, interference effects resulting from the superposition principle, delayed choice experiments, quantum measurements, the mechanism of quantization, the reason why entities can establish entanglement bonds and the statistical behaviour of indistinguishable entities. We further argue that the interpretation can also elucidate relativistic effects, focusing on time dilation. Finally, we suggest that it can provide a novel and challenging perspective on evolution. This article is the second in a two-part series devoted to exploring this promising approach to reality. The first part, which serves as a companion to this discussion, outlines the intellectual trajectory leading from the first applications of quantum notions to human cognition to the bold rethinking suggested by the conceptuality interpretation.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

arXiv:2412.19809•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Nov 27, 2025•3 citations

Transitions de phases à T = 0 dans les systèmes quantiques par le groupe de renormalisation dans l'espace réel

Rémi Jullien

The relevance of phase transition studies to the ground state of quantum systems is explained, and a real-space renormalization group method well adapted to such studies is described. The various improvements and extensions of the method are reviewed, with particular emphasis, in terms of applications, on the study of frustration in quantum systems, the study of interacting fermion systems (Hubbard model, Kondo lattice model), and the study of disordered systems.[Journal translation]

Canadian Journal of Physics•May 1, 1981•26 citations
This is a conceptual paper that re-examines the principles underlying the application of renormalization theory to quantum phase transitions in the light of quantum information theory. We start by describing the intuitive argument known as the Kadanoff ``block-spin'' construction for spins fixed on a lattice and then outline some subsequent ideas by Wilson and White. We then reconstruct these concepts for quantum phase transitions from first principles. This new perspective offers some very natural explanations for some features of renormalization theory that had previously seemed rather mysterious, even contrived. It also offers some suggestions as to how we might modify renormalization methods to make them more successful. We then discuss some possible order parameters and a class of functionals that are analogues of the correlation length in such systems.
Abstract Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.
The primary goal of modern theories of critical phenomena is the evaluation of critical exponents from first principles, implying the need to get beyond mean field theories which predict the same exponents independent of the nature of the system. This chapter focuses on a new approach emerged in the 1960s based on two ideas—scaling and renormalization. It presents the physical picture developed by L. P. Kadanoff that provides a conceptual basis for scaling and which has become part of the standard language of critical phenomena. Renormalization provides a way to calculate the free energy not involving a direct evaluation of the partition function—it's a new paradigm in statistical mechanics. The chapter analyzes a simplified, approximate set of recursion relations valid at high temperature for a model with nearest and next-nearest-neighbor interactions. In 1971 K. G. Wilson published two articles marking the introduction of the renormalization group to the study of critical phenomena.
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of one hundred and fifty years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behavior separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications are summarized.
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of quenched disorder on the quantum phase transitions is also discussed. The review is performed within the framework of the thermodynamic scaling theory and by the most general methods of statistical physics for the treatment of phase transitions: general lengthscale arguments, exact solutions, mean field approximation, Hubbard-Stratonovich transformation, Feynman path integral approach, and renormalization group in the field theoretical variant. Some new ideas and results are presented. Outstanding theoretical problems are mentioned. 1.
An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies Heisenberg's uncertainty principle, wave function-based and entanglement-based non-locality, interference effects resulting from the superposition principle, delayed choice experiments, quantum measurements, the mechanism of quantization, the reason why entities can establish entanglement bonds and the statistical behaviour of indistinguishable entities. We further argue that the interpretation can also elucidate relativistic effects, focusing on time dilation. Finally, we suggest that it can provide a novel and challenging perspective on evolution. This article is the second in a two-part series devoted to exploring this promising approach to reality. The first part, which serves as a companion to this discussion, outlines the intellectual trajectory leading from the first applications of quantum notions to human cognition to the bold rethinking suggested by the conceptuality interpretation.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.