Publications

Order by: publication date number of citations

• Deriving density-matrix functionals for excited states

  Julia Liebert, Christian Schilling

  SciPost Phys. 14, 120 (2023) · published 19 May 2023 | Toggle abstract · pdf

  We initiate the recently proposed $w$-ensemble one-particle reduced density matrix functional theory ($w$-RDMFT) by deriving the first functional approximations and illustrate how excitation energies can be calculated in practice. For this endeavour, we first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. Second, due to the particular suitability of $w$-RDMFT for describing Bose-Einstein condensates, we demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states. Our findings highlight the physical relevance of the generalized exclusion principle for fermionic and bosonic mixed states and the curse of universality in functional theories.

  10 citations

• Hamiltonian Truncation Effective Theory

  Timothy Cohen, Kara Farnsworth, Rachel Houtz, Markus A. Luty

  SciPost Phys. 13, 011 (2022) · published 4 August 2022 | Toggle abstract · pdf

  Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of $H_0/E_\text{max}$. The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda \phi^4$ theory, and compute the the leading $1/E_\text{max}^2$ corrections to the effective Hamiltonian. We show that these corrections non-trivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_\text{max}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda \phi^4$ theory and perform calculations that demonstrate the separation of scales in this theory.

  10 citations

• If the weak were strong and the strong were weak

  Nakarin Lohitsiri, David Tong

  SciPost Phys. 7, 059 (2019) · published 8 November 2019 | Toggle abstract · pdf

  We explore the phase structure of the Standard Model as the relative strengths of the SU(2) weak force and SU(3) strong force are varied. With a single generation of fermions, the structure of chiral symmetry breaking suggests that there is no phase transition as we interpolate between the SU(3)-confining phase and the SU(2)-confining phase. Remarkably, the massless left-handed neutrino, familiar in our world, morphs smoothly into a massless right-handed down-quark. With multiple generations, a similar metamorphosis occurs, but now proceeding via a phase transition. In the second half of the paper we introduce a two-parameter extension of the Standard Model, a chiral gauge theory with gauge group U(1) x Sp(r) x SU(N). We again explore the phase structure of the theory as the relative strengths of the Sp(r) and SU(N) gauge couplings vary.

  10 citations

• Phonon redshift and Hubble friction in an expanding BEC

  Stephen Eckel, Ted Jacobson

  SciPost Phys. 10, 064 (2021) · published 11 March 2021 | Toggle abstract · pdf

  We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.

  10 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.

  10 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.

  10 citations

• Exceptional points in the Baxter-Fendley free parafermion model

  Robert A. Henry, Murray T. Batchelor

  SciPost Phys. 15, 016 (2023) · published 19 July 2023 | Toggle abstract · pdf

  Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to $\mathbb{Z}_N$-symmetric clock models. In 1989 Baxter discovered a non-Hermitian but $\mathcal{PT}$-symmetric model directly generalising the Ising chain, which was later described by Fendley as a free parafermion spectrum. By extending the model's magnetic field parameter to the complex plane, it is shown that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general $\mathcal{PT}$-symmetric at these exceptional points, their proximity can have a profound impact on the model on the $\mathcal{PT}$-symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

  10 citations

• To profile or to marginalize - A SMEFT case study

  Ilaria Brivio, Sebastian Bruggisser, Nina Elmer, Emma Geoffray, Michel Luchmann, Tilman Plehn

  SciPost Phys. 16, 035 (2024) · published 29 January 2024 | Toggle abstract · pdf

  Global SMEFT analyses have become a key interpretation framework for LHC physics, quantifying how well a large set of kinematic measurements agrees with the Standard Model. This agreement is encoded in measured Wilson coefficients and their uncertainties. A technical challenge of global analyses are correlations. We compare, for the first time, results from a profile likelihood and a Bayesian marginalization for a given data set with a comprehensive uncertainty treatment. Using the validated Bayesian framework we analyse a series of new kinematic measurements. For the updated dataset we find and explain differences between the marginalization and profile likelihood treatments.

  10 citations

• Engineered Josephson diode effect in kinked Rashba nanochannels

  Alfonso Maiellaro, Mattia Trama, Jacopo Settino, Claudio Guarcello, Francesco Romeo, Roberta Citro

  SciPost Phys. 17, 101 (2024) · published 2 October 2024 | Toggle abstract · pdf

  The superconducting diode effect, reminiscent of the unidirectional charge transport in semiconductor diodes, is characterized by a nonreciprocal, dissipationless flow of Cooper pairs. This remarkable phenomenon arises from the interplay between symmetry constraints and the inherent quantum behavior of superconductors. Here, we explore the geometric control of the diode effect in a kinked nanostrip Josephson junction based on a two-dimensional electron gas (2DEGs) with Rashba spin-orbit interaction. We provide a comprehensive analysis of the diode effect as a function of the kink angle and the out-of-plane magnetic field. Our analysis reveals a rich phase diagram, showcasing a geometry and field-controlled diode effect. The phase diagram also reveals the presence of an anomalous Josephson effect related to the emergence of trivial zero-energy Andreev bound states, which can evolve into Majorana bound states. Our findings indicate that the exceptional synergy between geometric control of the diode effect and topological phases can be effectively leveraged to design and optimize superconducting devices with tailored transport properties.

  10 citations

• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

  Friethjof Theel, Simeon I. Mistakidis, Peter Schmelcher

  SciPost Phys. 16, 023 (2024) · published 23 January 2024 | Toggle abstract · pdf

  We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and a trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

  10 citations