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Andrea Trombettoni23/09/2024, 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 ฮณ(x), x belonging to a general bounded , compact, domain ฮฉ. ฮณ(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...
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Gonzalo De Polsi23/09/2024, 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...
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Ivan Balog23/09/2024, 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 $\varphi^4$...
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Fรฉlix Rose23/09/2024, 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...
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David K. Campbell23/09/2024, 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...
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Mireia Tolosa Simeon23/09/2024, 16:50
The chiral Ising-, XY-, and Heisenberg models serve as effective descriptions of Dirac
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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... -
Patrick Jentsch23/09/2024, 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...
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Niklas Zorbach23/09/2024, 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...
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Andrey Katanin24/09/2024, 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...
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Robin Scholle24/09/2024, 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 Nรฉel, stripe and spiral order. I will give a short summary of the method followed by a presentation of our current results and a possible...
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Shunsuke Yabunaka24/09/2024, 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...
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Kilian Fraboulet25/09/2024, 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, โฆ). The...
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40. Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the fRGMiriam Patricolo25/09/2024, 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...
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Dominique Mouhanna25/09/2024, 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...
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Pawel Jakubczyk25/09/2024, 15:30
We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector Qโ=0โ. 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...
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Nikolaos Parthenios25/09/2024, 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...
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Martin Hasenbusch25/09/2024, 16:50
The accurate determination of universal quantities, such as critical exponents,
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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... -
Andreas Rรผckriegel25/09/2024, 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...
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Liubov Gosteva25/09/2024, 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...
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Peter Kopietz26/09/2024, 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...
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Lasse Gresista26/09/2024, 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....
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Nepomuk Ritz26/09/2024, 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...
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Jonas Profe26/09/2024, 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...
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