12th International Conference on the Exact Renormalization Group 2024 (ERG2024)

Session

Parallel B

23 Sept 2024, 14:30

Maison des Congrès

8. Critical geometry approach to phase transitions

Andrea Trombettoni

23/09/2024, 14:30

We devise a geometric description of bounded systems at criticality in dimension d (including d=3) [1]. This is achieved by altering the flat metric with a space dependent scale factor γ(x), x belonging to a general bounded , compact, domain Ω. γ(x) is chosen in order to have a scalar curvature to be constant and negative, the proper notion of curvature being -- as called in the mathematics...

10. Conformal constraints and the derivative expansion

Gonzalo De Polsi

23/09/2024, 14:50

In the last two decades, the derivative expansion has been employed with great success to compute physical quantities in critical phenomena within the non-perturbative renormalization group. This success was achieved by implementing the approximation scheme to high orders which brought, alongside, various conceptual insights regarding its behaviour. The general idea relies on finding fixed...

14. Instantons within the Functional renormalization group

Ivan Balog

23/09/2024, 15:10

As spatial dimensionality gets lower it becomes more difficult for a system to order. At some dimensionality, the so called lower critical dimension, the fluctuations prevent ordering all together and the only way to order is to put temperature to 0. We discuss the scenario of the approach to lower critical dimension within the Functional renormalization group (FRG) for the scalar $\varphi^4$...

12. Probability distribution function of the 2d Ising order parameter

Félix Rose

23/09/2024, 15:30

The question of the probability distribution of the sum of random variables has suscited considerable attention from various fields of physics and mathematics. While the case of uncorrelated variables is described by the central limit theorem and its extensions, that of strongly correlated variables is more complicated. Turning our attention to the canonical example of strongly correlated...

18. Multiscale Functional Renormalization Group Approach to the 1D Extended Hubbard Model

David K. Campbell

23/09/2024, 16:20

We review our recent development of the Multiscale Functional Renormalization Group (MFRG) as an approach to the study of strongly correlated electronic materials in which both electron-electron (e-e) and electron-phonon (e-ph) interactions play important roles. Our MFRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi...

46. Quantum critical Dirac semimetals and finite-temperature effects

Mireia Tolosa Simeon

23/09/2024, 16:50

The chiral Ising-, XY-, and Heisenberg models serve as effective descriptions of Dirac
semimetals undergoing a quantum phase transition into a symmetry-broken ordered
state. Interestingly, their quantum critical points govern the physical behavior of the system in the vicinity of the transition even at finite temperatures. In this contribution,
we explore the chiral models at...

20. New universality class describes Vicsek's flocking phase in physical dimensions

Patrick Jentsch

23/09/2024, 17:20

The Vicsek simulation model of flocking together with its theoretical treatment by Toner and Tu in 1995 were two foundational cornerstones of active matter physics. However, despite the field's tremendous progress, the actual universality class (UC) governing the scaling behavior of Viscek's "flocking" phase remains elusive. Here, we use nonperturbative, functional renormalization group...

110. Optimization and Stabilization of Functional Renormalization Group Flows

Niklas Zorbach

23/09/2024, 17:40

We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order existing regularization schemes with respect to the stability of renormalization group flows. Moreover, the order relation can be used to construct new regulators...

111. Local 2PI vertex approximation: Nanoflakes, ferromagnets, and SU(2) gauge theory for antiferromagnets

Andrey Katanin

24/09/2024, 16:40

I discuss application of local 2PI Vertex Approximation (also known as a coupled ladder approximation) to description of charge, spin instabilities in graphene nanoflakes, as well as spin instabilities in magnetic systems. In graphene nanoflakes for strong on-site repulsion the spin density wave instability is obtained, while for strong non-local interaction the charge density wave instability...

29. The zoo of states in the 2D Hubbard model

Robin Scholle

24/09/2024, 17:10

We use a combination of real-space Hartree-Fock theory and functional renormalization group to unbiasedly construct a phase diagram of the 2D Hubbard model in Temperature and Doping. We are able to detect various spin- and charge order patterns including Néel, stripe and spiral order. I will give a short summary of the method followed by a presentation of our current results and a possible...

31. Full potential approach to frustrated antiferromagnets

Shunsuke Yabunaka

24/09/2024, 17:40

We revisit the critical behavior of classical frustrated systems using the nonperturbative renormalization group (NPRG) equation. Our study is performed within the local potential approximation of this equation to which is added the flow of the field renormalization. Our flow equations are functional to avoid possible artifacts coming from field expansions which consists in keeping only a...

38. Bosonization for fermionic fRG at weak and strong couplings

Kilian Fraboulet

25/09/2024, 14:30

The vertex expansion of the Wetterich equation provides a reliable perturbative approach for purely fermionic systems, already at the 1-loop level. The conventional 1-loop truncation can be improved by means of the multiloop functional renormalization group (fRG) which relies on flow equations derived from self-consistent equations for the flowing vertices (Bethe-Salpeter equation, …). The...

40. Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the fRG

Miriam Patricolo

25/09/2024, 14:50

We extend the recently introduced single-boson exchange (SBE) formulation to the computation of the self-energy from the Schwinger-Dyson equation. In particular, we derive its general expression both in diagrammatic and in physical channels and show that the SBE formulation of the Schwinger-Dyson equation can be naturally applied also to non-local interactions. We furthermore discuss its...

42. The role of quenched disorder in polymerized membranes

Dominique Mouhanna

25/09/2024, 15:10

I review recent studies aiming to understand the effects of quenched disorder on polymerized membranes. This concerns both the ordered - flat - phase of membranes that is relevant for graphene and graphene-like materials and the crumpled-to-flat transition that takes place in generic polymerized membranes. I show that perturbative together with nonperturbative approaches provide a unified view...

44. Generalized Hertz action for quantum criticality in Fermi systems

Pawel Jakubczyk

25/09/2024, 15:30

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector Q⃗=0⃗. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian...

45. Secondary instabilities of 2D altermagnets

Nikolaos Parthenios

25/09/2024, 16:20

We explore the possible weak coupling instabilities of the 2D Hubbard model with existing altermagnetic order, within a truncated unity functional renormalization group (tUfRG) framework. We find that as a function of chemical potential the system exhibits instabilities towards distinct SDW orders that coexist with the altermagnetic order. We also find that the system exhibits superconducting...

48. Accurate estimates of universal quantities: Monte Carlo simulations of improved lattice models and finite size scaling

Martin Hasenbusch

25/09/2024, 16:50

The accurate determination of universal quantities, such as critical exponents,
by using high temperature series expansions or Monte Carlo simulations of
lattice models is hampered by corrections to scaling.
In [J. H. Chen, M. E. Fisher and B. G. Nickel, Phys. Rev. Lett. 48, 630 (1982)]
the authors suggested to study one parameter families of models.
The amplitudes of corrections to...

50. Phase diagram of the J1-J2 quantum Heisenberg model for arbitrary spin

Andreas Rückriegel

25/09/2024, 17:20

We use the spin functional renormalization group to investigate the J1-J2 quantum Heisenberg model on a square lattice. By incorporating sum rules associated with the fixed length of the spin operators as well as the nontrivial quantum dynamics implied by the spin algebra, we are able to compute the ground state phase diagram for arbitrary spin S, including the quantum paramagnetic phase at...

72. The inviscid fixed point of the multi-dimensional Burgers-KPZ equation

Liubov Gosteva

25/09/2024, 17:40

A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations [1]. This scaling was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been...

57. Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility

Peter Kopietz

26/09/2024, 14:30

We show that the high-temperature expansion of the free energy and arbitrary connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly...

59. Quantum effects on unconventional pinch-point singularities from pseudo-fermion functional renormalization

Lasse Gresista

26/09/2024, 14:50

The discovery of emergent gauge theories in condensed matter systems is associated with novel phenomena such as fractionalization and topological excitations. A prime example are spin ice compounds, which are materials hosting a ground state described by an emergent U(1) gauge theory, featuring monopole excitations arising from the fractionalization of microscopic spin degrees of freedom....

61. Real-frequency quantum field theory applied to the single-impurity Anderson model

Nepomuk Ritz

26/09/2024, 15:10

A major challenge in the field of correlated electrons is the computation of dynamical correlation functions. For comparisons with experiment, one is interested in their real-frequency dependence. This is difficult to compute because imaginary-frequency data from the Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum field theory to the...

63. divERGe - an open source functional renormalization code for material calculations

Jonas Profe

26/09/2024, 15:30

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU2 models in all of the...