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:2412.11619 · Physica Scripta

Time-translation invariance symmetry breaking hidden by finite-scale singularities

Ixandra Achitouv, Vincent Lahoche, Dine Ousmane Samary, Parham Radpay

Published Mar 3, 2026• 1 citation
arXivHTMLPDF

Abstract

Abstract In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean R N space through the complex landscape provided by a disordered Hamiltonian of type ‘2 + p ’. We focus on the large N limit, where the coarse-graining procedure is unconventional: it is based on the Wigner spectrum of the rank-2 disorder. The main consequence of this choice is that canonical dimensions depend on the scale, and the flow equations fail to become autonomous, preventing the existence of global fixed points. One of the main features of the underlying renormalization group flow is the existence of finite-scale singularities for initial conditions sufficiently close to the Gaussian region and for rank- p disorder intensity large enough. Using the Luttinger-Ward formalism, we show that these finite-scale singularities hide (and should be resolved by) a phase transition that breaks time-translation invariance.

DOI
10.1088/1402-4896/ae4cd1

Related papers

Large time effective kinetics $β$-functions for quantum (2 + p)-spin glass II: Effective vertex expansion, local potential approximation and symmetries

Bêm-Biéri Barthélémy Natta, Vincent Lahoche, Dine Ousmane Samary +1 more

This paper aims to study the functional renormalization group for quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$. By fixing the gauge symmetry in the construction of the FRG, that breaks the $O(N)$-symmetry and deriving the corresponding non-trivial Ward identity we can: In the first time coarse grain and focus on this study using a more attractive method such as the effective vertex expansion, and in the second time explore this model beyond the symmetry phase. We show finite scale singularities due to the disorder, interpreted as the signal in the perturbation theory. The unconventional renormalization group approach is based on coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic term, with an eigenvalue distribution following a deterministic law in the large $N$ limit. As an illustration, the case where $p=3$ is scrutinized.

arXiv:2411.11089•Nov 17, 2024•0 citations

Functional renormalization group for “p = 2” like glassy matrices in the planar approximation I. Vertex expansion at equilibrium

Vincent Lahoche, Dine Ousmane Samary

In this paper, we study the equilibrium states of a N×N stochastic complex random matrix M, whose entries evolve in time accordingly with a Langevin equation including both Gaussian white noises and a linear disorder, materialized by the Wigner random matrices. In large N-limit, the disorders behave as effective kinetics, and we examine a coarse-graining over the Wigner spectrum accordingly with two different schemes that we call respectively “active” and “passive”. We then investigate explicit solutions of the nonperturbative renormalization group using vertex and derivative expansion, a simple way to deal with the nonlocal nature of the effective field theory at large N. Our main statement is the existence of well-behaved fixed point solutions and at least some evidence about a discontinuous (first order) phase transition between a condensed and a dilute phase. We finally interpret the resulting phase space regarding the out-of-equilibrium process related to the dynamical phase transitions.

arXiv:2403.07577•Nuclear Physics B•Jun 6, 2024•1 citation

Functional renormalization group for “p = 2” like glassy matrices in the planar approximation III. Equilibrium dynamics and beyond

Vincent Lahoche, Dine Ousmane Samary

This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities arising from the large N effective kinetics. We construct a regulator that does not break time-reversal symmetry and show that the resulting flow equations reduce to the equilibrium flow built in our previous works. Finally, we investigate the flow equations beyond the equilibrium dynamics assumption and study the stability of the perturbation around the fluctuation-dissipation theorem.

arXiv:2404.11915•Nuclear Physics B•Aug 10, 2024•1 citation

On the landscape of scale invariance in quantum mechanics

Daniel K. Brattan, O. Ovdat, Éric Akkermans

Abstract We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate numerically the existence of a universal quantum phase transition from a continuous scale invariant phase to a discrete scale invariant phase. Close to the critical point, the discrete scale invariant phase is characterised by an isolated, closed, attracting trajectory in renomalisation group space (a limit cycle). Moving in appropriate directions in the parameter space of couplings this picture is altered to one controlled by a quasi periodic attracting trajectory (a limit torus) or fixed points. We identify a direct relation between the critical point, the renormalisation group picture and the power laws characterising the zero energy wave functions.

arXiv:1804.10213•Journal of Physics A Mathematical and Theoretical•Sep 7, 2018•5 citations

Renormalization of Quantum Operations: Parity-Time Transition and Chaotic Flows

Atsushi Oyaizu, Hongchao Li, Masaya Nakagawa +1 more

The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement backaction, in which the notion of conserved energy is absent. Here, we extend the RG to cover nonunitary quantum dynamics governed by quantum operations. By performing coarse-graining in real time, we find that the competition between decoherence and coherent dynamics plays a decisive role in the behavior of the RG flow. In particular, we find that chaotic behavior without fixed points emerges in the RG flow when coherent dynamics is dominant, with the parity-time transition serving as a prototypical example. The measurement-induced parity-time transition belongs to the universality class of the one-dimensional Yang-Lee edge singularity, which serves as a guide for experimentally realizing imaginary fields in lattice spin systems with a quantum system.

cond-mat.stat-mechCross-listedarXiv:2605.10459•May 12, 2026•0 citations

Conformal symmetry

John Cardy

We saw in Chapter 3 that the hamiltonian for a System at a critical point flows under the renormalization group into a critical fixed point. Under a renormalization group transformation, the microscopic length scale is rescaled by a constant factor b , and so the coordinates of a given point, as measured in units of this length scale, transform according to r → b −1 r. This is called a scale transformation . Once the flows reach such a fixed point, the parameters of the hamiltonian no longer change, and it is said to be scale invariant . As well as being scale invariant, the fixed point hamiltonian usually possesses other spatial symmetries. For example, if the underlying model is defined on a lattice, so that its hamiltonian is invariant under lattice translations, the corresponding critical fixed point hamiltonian is generally invariant under arbitrary uniform translations. This is because terms which might be added to the hamiltonian which break the symmetry under continuous translations down to its subgroup of lattice translations are irrelevant at such a fixed point. Similarly, if the lattice model is invariant under a sufficiently large subgroup of the rotation group (for example, if the interactions in the x and y directions on a Square lattice are equal), then the fixed point hamiltonian enjoys full rotational invariance. As discussed on p.58, even if the interactions are anisotropic, rotational invariance may often be recovered by a suitable finite relative rescaling of the coordinates.

Cambridge University Press eBooks•Apr 26, 1996•0 citations
Abstract In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean R N space through the complex landscape provided by a disordered Hamiltonian of type ‘2 + p ’. We focus on the large N limit, where the coarse-graining procedure is unconventional: it is based on the Wigner spectrum of the rank-2 disorder. The main consequence of this choice is that canonical dimensions depend on the scale, and the flow equations fail to become autonomous, preventing the existence of global fixed points. One of the main features of the underlying renormalization group flow is the existence of finite-scale singularities for initial conditions sufficiently close to the Gaussian region and for rank- p disorder intensity large enough. Using the Luttinger-Ward formalism, we show that these finite-scale singularities hide (and should be resolved by) a phase transition that breaks time-translation invariance.
Large time effective kinetics βββ-functions for quantum (2 + p)-spin glass II: Effective vertex expansion, local potential approximation and symmetries
This paper aims to study the functional renormalization group for quantum (2+p)(2+p)(2+p)-spin dynamics of a NNN-vector x∈RN\textbf{x}\in \mathbb{R}^Nx∈RN. By fixing the gauge symmetry in the construction of the FRG, that breaks the O(N)O(N)O(N)-symmetry and deriving the corresponding non-trivial Ward identity we can: In the first time coarse grain and focus on this study using a more attractive method such as the effective vertex expansion, and in the second time explore this model beyond the symmetry phase. We show finite scale singularities due to the disorder, interpreted as the signal in the perturbation theory. The unconventional renormalization group approach is based on coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic term, with an eigenvalue distribution following a deterministic law in the large NNN limit. As an illustration, the case where p=3p=3p=3 is scrutinized.
In this paper, we study the equilibrium states of a N×N stochastic complex random matrix M, whose entries evolve in time accordingly with a Langevin equation including both Gaussian white noises and a linear disorder, materialized by the Wigner random matrices. In large N-limit, the disorders behave as effective kinetics, and we examine a coarse-graining over the Wigner spectrum accordingly with two different schemes that we call respectively “active” and “passive”. We then investigate explicit solutions of the nonperturbative renormalization group using vertex and derivative expansion, a simple way to deal with the nonlocal nature of the effective field theory at large N. Our main statement is the existence of well-behaved fixed point solutions and at least some evidence about a discontinuous (first order) phase transition between a condensed and a dilute phase. We finally interpret the resulting phase space regarding the out-of-equilibrium process related to the dynamical phase transitions.
This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities arising from the large N effective kinetics. We construct a regulator that does not break time-reversal symmetry and show that the resulting flow equations reduce to the equilibrium flow built in our previous works. Finally, we investigate the flow equations beyond the equilibrium dynamics assumption and study the stability of the perturbation around the fluctuation-dissipation theorem.
Abstract We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate numerically the existence of a universal quantum phase transition from a continuous scale invariant phase to a discrete scale invariant phase. Close to the critical point, the discrete scale invariant phase is characterised by an isolated, closed, attracting trajectory in renomalisation group space (a limit cycle). Moving in appropriate directions in the parameter space of couplings this picture is altered to one controlled by a quasi periodic attracting trajectory (a limit torus) or fixed points. We identify a direct relation between the critical point, the renormalisation group picture and the power laws characterising the zero energy wave functions.
The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement backaction, in which the notion of conserved energy is absent. Here, we extend the RG to cover nonunitary quantum dynamics governed by quantum operations. By performing coarse-graining in real time, we find that the competition between decoherence and coherent dynamics plays a decisive role in the behavior of the RG flow. In particular, we find that chaotic behavior without fixed points emerges in the RG flow when coherent dynamics is dominant, with the parity-time transition serving as a prototypical example. The measurement-induced parity-time transition belongs to the universality class of the one-dimensional Yang-Lee edge singularity, which serves as a guide for experimentally realizing imaginary fields in lattice spin systems with a quantum system.
We saw in Chapter 3 that the hamiltonian for a System at a critical point flows under the renormalization group into a critical fixed point. Under a renormalization group transformation, the microscopic length scale is rescaled by a constant factor b , and so the coordinates of a given point, as measured in units of this length scale, transform according to r → b −1 r. This is called a scale transformation . Once the flows reach such a fixed point, the parameters of the hamiltonian no longer change, and it is said to be scale invariant . As well as being scale invariant, the fixed point hamiltonian usually possesses other spatial symmetries. For example, if the underlying model is defined on a lattice, so that its hamiltonian is invariant under lattice translations, the corresponding critical fixed point hamiltonian is generally invariant under arbitrary uniform translations. This is because terms which might be added to the hamiltonian which break the symmetry under continuous translations down to its subgroup of lattice translations are irrelevant at such a fixed point. Similarly, if the lattice model is invariant under a sufficiently large subgroup of the rotation group (for example, if the interactions in the x and y directions on a Square lattice are equal), then the fixed point hamiltonian enjoys full rotational invariance. As discussed on p.58, even if the interactions are anisotropic, rotational invariance may often be recovered by a suitable finite relative rescaling of the coordinates.