Publications

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• 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.

  58 citations

• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

  Isabelle Bouchoule, Benjamin Doyon, Jerome Dubail

  SciPost Phys. 9, 044 (2020) · published 2 October 2020 | Toggle abstract · pdf

  We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.

  58 citations

• Reconstructing the graviton

  Alfio Bonanno, Tobias Denz, Jan M. Pawlowski, Manuel Reichert

  SciPost Phys. 12, 001 (2022) · published 4 January 2022 | Toggle abstract · pdf

  We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

  57 citations

• Non-Standard neutrino interactions and neutral gauge bosons

  Julian Heeck, Manfred Lindner, Werner Rodejohann, Stefan Vogl

  SciPost Phys. 6, 038 (2019) · published 27 March 2019 | Toggle abstract · pdf

  We investigate Non-Standard Neutrino Interactions (NSI) arising from a flavor-sensitive $Z'$ boson of a new $U(1)'$ symmetry. We compare the limits from neutrino oscillations, coherent elastic neutrino--nucleus scattering, and $Z'$ searches at different beam and collider experiments for a variety of straightforward anomaly-free $U(1)'$ models generated by linear combinations of $B-L$ and lepton-family-number differences $L_\alpha-L_\beta$. Depending on the flavor structure of those models it is easily possible to avoid NSI signals in long-baseline neutrino oscillation experiments or change the relative importance of the various experimental searches. We also point out that kinetic $Z$-$Z'$ mixing gives vanishing NSI in long-baseline experiments if a direct coupling between the $U(1)'$ gauge boson and matter is absent. In contrast, $Z$-$Z'$ mass mixing generates such NSI, which in turn means that there is a Higgs multiplet charged under both the Standard Model and the new $U(1)'$ symmetry.

  56 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.

  56 citations

• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

  David J. Luitz, Ivan M. Khaymovich, Yevgeny Bar Lev

  SciPost Phys. Core 2, 006 (2020) · published 30 April 2020 | Toggle abstract · pdf

  The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.

  56 citations

• Detecting a many-body mobility edge with quantum quenches

  Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde

  SciPost Phys. 1, 010 (2016) · published 27 October 2016 | Toggle abstract · pdf

  The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

  55 citations

• Full counting statistics in the transverse field Ising chain

  Stefan Groha, Fabian H. L. Essler, Pasquale Calabrese

  SciPost Phys. 4, 043 (2018) · published 28 June 2018 | Toggle abstract · pdf

  We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general Gaussian states. We consider applications to the full counting statistics in the ground state, finite temperature equilibrium states, non-equilibrium steady states and time evolution after global quantum quenches. We derive an analytical expression for the time and subsystem size dependence of the characteristic function at sufficiently late times after a quantum quench. This expression features an interesting multiple light-cone structure.

  54 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.

  54 citations

• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties

  Lenart Zadnik, Maurizio Fagotti

  SciPost Phys. Core 4, 010 (2021) · published 29 April 2021 | Toggle abstract · pdf

  We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.

  54 citations