Publications

Order by: publication date number of citations

• Discrete theta angles, symmetries and anomalies

  Po-Shen Hsin, Ho Tat Lam

  SciPost Phys. 10, 032 (2021) · published 12 February 2021 | Toggle abstract · pdf

  Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and 't Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d QCD with $SU(N),SU(N)/\mathbb{Z}_k$ or $SO(N)$ gauge groups as well as various 3d and 2d gauge theories.

  69 citations

• A constructive theory of the numerically accessible many-body localized to thermal crossover

  Philip J D Crowley, Anushya Chandran

  SciPost Phys. 12, 201 (2022) · published 24 June 2022 | Toggle abstract · pdf

  The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

  69 citations

• Goldstone modes and photonization for higher form symmetries

  Diego M. Hofman, Nabil Iqbal

  SciPost Phys. 6, 006 (2019) · published 14 January 2019 | Toggle abstract · pdf

  We discuss generalized global symmetries and their breaking. We extend Goldstone's theorem to higher form symmetries by showing that a perimeter law for an extended $p$-dimensional defect operator charged under a continuous $p$-form generalized global symmetry necessarily results in a gapless mode in the spectrum. We also show that a $p$-form symmetry in a conformal theory in $2(p+1)$ dimensions has a free realization. In four dimensions this means any 1-form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics, i.e. the current can be photonized. The photonized theory has infinitely many conserved 0-form charges that are constructed by integrating the symmetry currents against suitable 1-forms. We study these charges by developing a twistor-based formalism that is a 4d analogue of the usual holomorphic complex analysis familiar in $CFT_2$. The charges are shown to obey an algebra with central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for higher form symmetries.

  68 citations

• Algebraic theory of quantum synchronization and limit cycles under dissipation

  Berislav Buča, Cameron Booker, Dieter Jaksch

  SciPost Phys. 12, 097 (2022) · published 17 March 2022 | Toggle abstract · pdf

  Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

  68 citations

• Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

  Sean Vig, Anshul Kogar, Matteo Mitrano, Ali A. Husain, Vivek Mishra, Melinda S. Rak, Luc Venema, Peter D. Johnson, Genda D. Gu, Eduardo Fradkin, Michael R. Norman, Peter Abbamonte

  SciPost Phys. 3, 026 (2017) · published 6 October 2017 | Toggle abstract · pdf

  One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $\chi({\bf q},\omega)$. The imaginary part, $\chi''({\bf q},\omega)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $\chi$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure $\chi({\bf q},\omega)$ at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure $\chi$ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as ``M-EELS" allows direct measurement of $\chi''({\bf q},\omega)$ with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-{\bf q} excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.

  68 citations

• Twisted and untwisted negativity spectrum of free fermions

  Hassan Shapourian, Paola Ruggiero, Shinsei Ryu, Pasquale Calabrese

  SciPost Phys. 7, 037 (2019) · published 25 September 2019 | Toggle abstract · pdf

  A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

  67 citations

• Machine learning and LHC event generation

  Anja Butter, Tilman Plehn, Steffen Schumann, Simon Badger, Sascha Caron, Kyle Cranmer, Francesco Armando Di Bello, Etienne Dreyer, Stefano Forte, Sanmay Ganguly, Dorival Gonçalves, Eilam Gross, Theo Heimel, Gudrun Heinrich, Lukas Heinrich, Alexander Held, Stefan Höche, Jessica N. Howard, Philip Ilten, Joshua Isaacson, Timo Janßen, Stephen Jones, Marumi Kado, Michael Kagan, Gregor Kasieczka, Felix Kling, Sabine Kraml, Claudius Krause, Frank Krauss, Kevin Kröninger, Rahool Kumar Barman, Michel Luchmann, Vitaly Magerya, Daniel Maitre, Bogdan Malaescu, Fabio Maltoni, Till Martini, Olivier Mattelaer, Benjamin Nachman, Sebastian Pitz, Juan Rojo, Matthew Schwartz, David Shih, Frank Siegert, Roy Stegeman, Bob Stienen, Jesse Thaler, Rob Verheyen, Daniel Whiteson, Ramon Winterhalder, Jure Zupan

  SciPost Phys. 14, 079 (2023) · published 21 April 2023 | Toggle abstract · pdf

  First-principle simulations are at the heart of the high-energy physics research program. They link the vast data output of multi-purpose detectors with fundamental theory predictions and interpretation. This review illustrates a wide range of applications of modern machine learning to event generation and simulation-based inference, including conceptional developments driven by the specific requirements of particle physics. New ideas and tools developed at the interface of particle physics and machine learning will improve the speed and precision of forward simulations, handle the complexity of collision data, and enhance inference as an inverse simulation problem.

  67 citations

• Krylov complexity of many-body localization: Operator localization in Krylov basis

  Fabian Ballar Trigueros, Cheng-Ju Lin

  SciPost Phys. 13, 037 (2022) · published 29 August 2022 | Toggle abstract · pdf

  We study the operator growth problem and its complexity in the many-body localization (MBL) system from the Lanczos algorithm perspective. Using the Krylov basis, the operator growth problem can be viewed as a single-particle hopping problem on a semi-infinite chain with the hopping amplitudes given by the Lanczos coefficients. We find that, in the MBL systems, the Lanczos coefficients scale as ∼ n/ ln(n) asymptotically, same as in the ergodic systems, but with an additional even-odd alteration and an effective randomness. We use a simple linear extrapolation scheme as an attempt to extrapolate the Lanczos coefficients to the thermodynamic limit. With the original and extrapolated Lanczos coefficients, we study the properties of the emergent single-particle hopping problem via its spectral function, integrals of motion, Krylov complexity, wavefunction profile and return probability. Our numerical results of the above quantities suggest that the emergent single-particle hopping problem in the MBL system is localized when initialized on the first site. We also study the operator growth in the MBL phenomenological model, whose Lanczos coefficients also have an even-odd alteration, but approach constants asymptotically. The Krylov complexity grows linearly in time in this case.

  67 citations

• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

  Giuseppe De Tomasi, Mohsen Amini, Soumya Bera, Ivan M. Khaymovich, Vladimir E. Kravtsov

  SciPost Phys. 6, 014 (2019) · published 30 January 2019 | Toggle abstract · pdf

  We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probability of finding the initial state after time $t$. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of $R(t)$ with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of $R(t\to\infty)=k$, finite in the thermodynamic limit $N\rightarrow\infty$, which approaches $k=R(t\to 0)$ in this limit.

  66 citations

• The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code

  Martin Bercx, Florian Goth, Johannes S. Hofmann, Fakher F. Assaad

  SciPost Phys. 3, 013 (2017) · published 16 August 2017 · licensed under CC BY-SA (4.0) | Toggle abstract · pdf

  The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the $SU(N)$-Hubbard-Heisenberg model. One can download the code from our Git instance at https://alf.physik.uni-wuerzburg.de and sign in to file issues.

  65 citations