Publications

Order by: publication date number of citations

• Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

  Oleksandr Gamayun, Oleg Lychkovskiy, Jean-Sébastien Caux

  SciPost Phys. 8, 036 (2020) · published 5 March 2020 | Toggle abstract · pdf

  We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

  31 citations

• Non-unitary dynamics of Sachdev-Ye-Kitaev chain

  Chunxiao Liu, Pengfei Zhang, Xiao Chen

  SciPost Phys. 10, 048 (2021) · published 23 February 2021 | Toggle abstract · pdf

  We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

  31 citations

• Renormalization group consistency and low-energy effective theories

  Jens Braun, Marc Leonhardt, Jan M. Pawlowski

  SciPost Phys. 6, 056 (2019) · published 9 May 2019 | Toggle abstract · pdf

  Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are consistent quantum field theories by themselves and can be embedded in QCD, but typically have a physical ultraviolet cutoff that restricts their range of validity. Here, we provide a discussion of the concept of renormalization group consistency, aiming at an analysis of cutoff effects and regularization-scheme dependences in general studies of low-energy effective theories. For illustration, our findings are applied to low-energy effective models of QCD in different approximations including the mean-field approximation. More specifically, we consider hot and dense as well as finite systems and demonstrate that violations of renormalization group consistency affect significantly the predictive power of the corresponding model calculations.

  31 citations

• Quantum field theory and the Bieberbach conjecture

  Parthiv Haldar, Aninda Sinha, Ahmadullah Zahed

  SciPost Phys. 11, 002 (2021) · published 8 July 2021 | Toggle abstract · pdf

  An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and the non-perturbative crossing symmetric representation of 2-2 scattering amplitudes of identical scalars is pointed out. Using the dispersion relation and unitarity, we are able to derive several inequalities, analogous to those which arise in the discussions of the Bieberbach conjecture. We derive new and strong bounds on the ratio of certain Wilson coefficients and demonstrate that these are obeyed in one-loop $\phi^4$ theory, tree level string theory as well as in the S-matrix bootstrap. Further, we find two sided bounds on the magnitude of the scattering amplitude, which are shown to be respected in all the contexts mentioned above. Translated to the usual Mandelstam variables, for large $|s|$, fixed $t$, the upper bound reads $|\mathcal{M}(s,t)|\lesssim |s^2|$. We discuss how Szegö's theorem corresponds to a check of univalence in an EFT expansion, while how the Grunsky inequalities translate into nontrivial, nonlinear inequalities on the Wilson coefficients.

  31 citations

• Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics

  Shiyu Zhou, Zhi-Cheng Yang, Alioscia Hamma, Claudio Chamon

  SciPost Phys. 9, 087 (2020) · published 14 December 2020 | Toggle abstract · pdf

  Clifford circuits are insufficient for universal quantum computation or creating $t$-designs with $t\ge 4$. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T $(\pi/8)$ gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.

  31 citations

• Non-boost invariant fluid dynamics

  Jan de Boer, Jelle Hartong, Emil Have, Niels A. Obers, Watse Sybesma

  SciPost Phys. 9, 018 (2020) · published 11 August 2020 | Toggle abstract · pdf

  We consider uncharged fluids without any boost symmetry on an arbitrary curved background and classify all allowed transport coefficients up to first order in derivatives. We assume rota- tional symmetry and we use the entropy current formalism. The curved background geometry in the absence of boost symmetry is called absolute or Aristotelian spacetime. We present a closed-form expression for the energy-momentum tensor in Landau frame which splits into three parts: a dissipative (10), a hydrostatic non-dissipative (2) and a non-hydrostatic non- dissipative part (4), where in parenthesis we have indicated the number of allowed transport coefficients. The non-hydrostatic non-dissipative transport coefficients can be thought of as the generalization of coefficients that would vanish if we were to restrict to linearized perturba- tions and impose the Onsager relations. For the two hydrostatic and the four non-hydrostatic non-dissipative transport coefficients we present a Lagrangian description. Finally when we impose scale invariance, thus restricting to Lifshitz fluids, we find 7 dissipative, 1 hydrostatic and 2 non-hydrostatic non-dissipative transport coefficients.

  31 citations

• A non-lorentzian primer

  Eric Bergshoeff, José Figueroa-O'Farrill, Joaquim Gomis

  SciPost Phys. Lect. Notes 69 (2023) · published 31 May 2023 | Toggle abstract · pdf

  We review both the kinematics and dynamics of non-lorentzian theories and their associated geometries. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras. Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations. We explain the relation with the coadjoint orbit method. We continue discussing three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity. Introducing matter, we discuss electric and magnetic non-lorentzian field theories for three different spins: spin-0, spin-1/2 and spin-1, as limits of relativistic theories.

  31 citations

• The grin of Cheshire cat resurgence from supersymmetric localization

  Daniele Dorigoni, Philip Glass

  SciPost Phys. 4, 012 (2018) · published 27 February 2018 | Toggle abstract · pdf

  First we compute the $\mbox{S}^2$ partition function of the supersymmetric $\mathbb{CP}^{N-1}$ model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the $\mathbb{CP}^1$ case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instanton-anti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from $N$ to $r\in\mathbb{R}$. Although for generic real $r$ supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer $r$ to recover the undeformed model.

  31 citations

• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

  Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

  SciPost Phys. 7, 025 (2019) · published 29 August 2019 | Toggle abstract · pdf

  We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

  31 citations

• A physical protocol for observers near the boundary to obtain bulk information in quantum gravity

  Chandramouli Chowdhury, Olga Papadoulaki, and Suvrat Raju

  SciPost Phys. 10, 106 (2021) · published 17 May 2021 | Toggle abstract · pdf

  We consider a set of observers who live near the boundary of global AdS, and are allowed to act only with simple low-energy unitaries and make measurements in a small interval of time. The observers are not allowed to leave the near-boundary region. We describe a physical protocol that nevertheless allows these observers to obtain detailed information about the bulk state. This protocol utilizes the leading gravitational back-reaction of a bulk excitation on the metric, and also relies on the entanglement-structure of the vacuum. For low-energy states, we show how the near-boundary observers can use this protocol to completely identify the bulk state. We explain why the protocol fails completely in theories without gravity, including non-gravitational gauge theories. This provides perturbative evidence for the claim that one of the signatures of holography --- the fact that information about the bulk is also available near the boundary --- is already visible in the low-energy theory of gravity.

  30 citations