Publications

Order by: publication date number of citations

• Essential renormalisation group

  Alessio Baldazzi, Riccardo Ben Alì Zinati, Kevin Falls

  SciPost Phys. 13, 085 (2022) · published 7 October 2022 | Toggle abstract · pdf

  We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with the task of computing only the flow of the essential ones. To achieve this aim, we utilise a renormalisation group equation for the effective average action which incorporates general non-linear field reparameterisations. A prominent feature of the scheme is that, apart from the renormalisation of the mass, the propagator evaluated at any constant value of the field maintains its unrenormalised form. Conceptually, the simplifications can be understood as providing a description based only on quantities that enter expressions for physical observables since the redundant, non-physical content is automatically disregarded. To exemplify the scheme's utility, we investigate the Wilson-Fisher fixed point in three dimensions at order two in the derivative expansion. In this case, the scheme removes all order $\partial^2$ operators apart from the canonical term. Further simplifications occur at higher orders in the derivative expansion. Although we concentrate on a minimal scheme that reduces the complexity of computations, we propose more general schemes where inessential couplings can be tuned to optimise a given approximation. We further discuss the applicability of the scheme to a broad range of physical theories.

  7 citations

• Statistical Floquet prethermalization of the Bose-Hubbard model

  Emanuele G. Dalla Torre, David Dentelski

  SciPost Phys. 11, 040 (2021) · published 24 August 2021 | Toggle abstract · pdf

  The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

  7 citations

• DCore: Integrated DMFT software for correlated electrons

  Hiroshi Shinaoka, Junya Otsuki, Mitsuaki Kawamura, Nayuta Takemori, Kazuyoshi Yoshimi

  SciPost Phys. 10, 117 (2021) · published 27 May 2021 | Toggle abstract · pdf

  We present a new open-source program, DCore, that implements dynamical mean-field theory (DMFT). DCore features a user-friendly interface based on text and HDF5 files. It allows DMFT calculations of tight-binding models to be performed on predefined lattices as well as \textit{ab initio} models constructed by external density functional theory codes through the Wannier90 package. Furthermore, DCore provides interfaces to many advanced quantum impurity solvers such as quantum Monte Carlo and exact diagonalization solvers. This paper details the structure and usage of DCore and shows some applications.

  7 citations

• Effects of intraspecific cooperative interactions in large ecosystems

  Ada Altieri, Giulio Biroli

  SciPost Phys. 12, 013 (2022) · published 11 January 2022 | Toggle abstract · pdf

  We analyze the role of the Allee effect, a positive correlation between population density and mean individual fitness, for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviours of ecosystems.

  7 citations

• Phase transitions above the upper critical dimension

  Bertrand Berche, Tim Ellis, Yurij Holovatch, Ralph Kenna

  SciPost Phys. Lect. Notes 60 (2022) · published 12 August 2022 | Toggle abstract · pdf

  These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous phase transitions, we discuss the apparent failure of the Gaussian fixed point to capture scaling for Landau mean-field theory, which should hold in the thermodynamic limit above $d_{\rm uc}$. We recount how Fisher's dangerous-irrelevant-variable formalism applied to thermodynamic functions partially repairs the situation but at the expense of hyperscaling and finite-size scaling, both of which were, until recently, believed not to apply above $d_{\rm uc}$. We recall limitations of various attempts to match the RG with analytical and numerical results for Ising systems. We explain how the extension of dangerous irrelevancy to the correlation sector is key to marrying the above concepts into a comprehensive RG scaling picture that renders hyperscaling and finite-size scaling valid in all dimensions. We collect what we believe is the current status of the theory, including some new insights and results. This paper is in grateful memory of Michael Fisher who introduced many of the concepts discussed and who, half a century later, contributed to their advancement.

  7 citations

• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet

  Andrew Smerald, Frederic Mila

  SciPost Phys. 5, 030 (2018) · published 28 September 2018 | Toggle abstract · pdf

  We study the triangular-lattice Ising model with dipolar interactions, inspired by its realisation in artificial arrays of nanomagnets. We show that a classical spin-liquid forms at intermediate temperatures, and that its behaviour can be tuned by temperature and/or a small lattice distortion between a string Luttinger liquid and a domain-wall-network state. At low temperature there is a transition into a magnetically ordered phase, which can be first-order or continous with a crossover in the critical behaviour between Pokrovsky-Talapov and 2D-Ising universality. When the Pokrovsky-Talapov criticality dominates, the transition is essentially of the Kasteleyn type.

  7 citations

• Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption

  Wei Chen, Gero von Gersdorff

  SciPost Phys. Core 5, 040 (2022) · published 16 August 2022 | Toggle abstract · pdf

  The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting point, we generalize these concepts by introducing dressed Berry curvature and quantum metric at finite temperature, in which the effect of many-body interactions can be included perturbatively. These quantities are extracted from the charge polarization susceptibility caused by linearly or circularly polarized electric fields, whose spectral functions can be measured from momentum-resolved exciton or infrared absorption rate. As a concrete example, we investigate Chern insulators in the presence of impurity scattering, whose results suggest that the quantum geometric properties are protected by the energy gap against many-body interactions.

  7 citations

• Simulating Floquet topological phases in static systems

  Selma Franca, Fabian Hassler, Ion Cosma Fulga

  SciPost Phys. Core 4, 007 (2021) · published 15 April 2021 | Toggle abstract · pdf

  We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not to suffer from decoherence and heating.

  7 citations

• Determination of the time scale of photoemission from the measurement of spin polarization

  Mauro Fanciulli, J. Hugo Dil

  SciPost Phys. 5, 058 (2018) · published 6 December 2018 | Toggle abstract · pdf

  The Eisenbud-Wigner-Smith (EWS) time delay of photoemission depends on the phase term of the matrix element describing the transition. Because of an interference process between partial channels, the photoelectrons acquire a spin polarization which is also related to the phase term. The analytical model for estimating the time delay by measuring the spin polarization is reviewed in this manuscript. In particular, the distinction between scattering EWS and interfering EWS time delay will be introduced, providing an insight in the chronoscopy of photoemission. The method is applied to the recent experimental data for Cu(111) presented in M. Fanciulli et al., PRL 118, 067402 (2017), allowing to give better upper and lower bounds and estimates for the EWS time delays.

  7 citations

• Delocalization transition in low energy excitation modes of vector spin glasses

  Silvio Franz, Flavio Nicoletti, Giorgio Parisi, Federico Ricci-Tersenghi

  SciPost Phys. 12, 016 (2022) · published 12 January 2022 | Toggle abstract · pdf

  We study the energy minima of the fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $m\ge 3$. The model has a zero temperature transition from a paramagnetic phase at high field to a spin glass phase at low field. We study the eigenvalues and eigenvectors of the Hessian in the minima of the Hamiltonian. The spectrum is gapless both in the paramagnetic and in the spin glass phase, with a pseudo-gap behaving as $\lambda^{m-1}$ in the paramagnetic phase and as $\sqrt{\lambda}$ at criticality and in the spin glass phase. Despite the long-range nature of the model, the eigenstates close to the edge of the spectrum display quasi-localization properties. We show that the paramagnetic to spin glass transition corresponds to delocalization of the edge eigenvectors. We solve the model by the cavity method in the thermodynamic limit. We also perform numerical minimization of the Hamiltonian for $N\le 2048$ and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

  7 citations