Related papers: The quantum $p$-spin renormalization group in the …
This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder,…
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…
We develop a thorough theoretical framework based on the nonperturvative renormalization group (RG) a la Wetterich to tackle the interplay of coupled fermionic and order-parameter fluctuations at metallic quantum critical points with…
In this paper, we study the equilibrium states of a $N\times N$ 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…
We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N…
The gravitational asymptotic safety program envisions a high-energy completion of the gravitational interactions by an interacting renormalization group fixed point, the Reuter fixed point. The primary tool for investigating this scenario…
Quantum field theory in curved spacetime is perhaps the most reliable framework in which one can investigate quantum effects in the presence of strong gravitational fields. Nevertheless, it is often studied by means of perturbative…
Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\cal N}=2$ supersymmetric…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
In this paper, we use a nonperturbative renormalization group approach to construct the dynamical phase space of a quantum spin glass in the large $N$ limit. The disordered Hamiltonian is of ``$2 + p$" type, and we perform a coarse-graining…
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…
This paper, as a continuation of our previous investigation [arXiv:2403.07577] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
Tensor models admit the large $N$ limit, dominated by the graphs called melons. The melons are characterized by the Gurau number $\varpi=0$ and the amplitude of the Feynman graphs are proportional to $N^{-\varpi}$. Other leading order…
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this…
This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…
We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start…