Publications

Order by: publication date number of citations

• Liberating confinement from Lagrangians: 1-form symmetries and lines in 4d N=1 from 6d N=(2,0)

  Lakshya Bhardwaj, Max Hübner, Sakura Schäfer-Nameki

  SciPost Phys. 12, 040 (2022) · published 26 January 2022 | Toggle abstract · pdf

  We study confinement in 4d N=1 theories obtained by deforming 4d N=2 theories of Class S. We argue that confinement in a vacuum of the N=1 theory is encoded in the 1-cycles of the associated N=1 curve. This curve is the spectral cover associated to a generalized Hitchin system describing the profiles of two Higgs fields over the Riemann surface upon which the 6d (2,0) theory is compactified. Using our method, we reproduce the expected properties of confinement in various classic examples, such as 4d N=1 pure Super-Yang-Mills theory and the Cachazo-Seiberg-Witten setup. More generally, this work can be viewed as providing tools for probing confinement in non-Lagrangian N=1 theories, which we illustrate by constructing an infinite class of non-Lagrangian N=1 theories that contain confining vacua. The simplest model in this class is an N=1 deformation of the N=2 theory obtained by gauging $SU(3)^3$ flavor symmetry of the $E_6$ Minahan-Nemeschansky theory.

  25 citations

• Kibble–Zurek mechanism in the Ising Field Theory

  Kristóf Hódsági, Marton Kormos

  SciPost Phys. 9, 055 (2020) · published 20 October 2020 | Toggle abstract · pdf

  The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

  25 citations

• $q$th-root non-Hermitian Floquet topological insulators

  Longwen Zhou, Raditya Weda Bomantara, Shenlin Wu

  SciPost Phys. 13, 015 (2022) · published 8 August 2022 | Toggle abstract · pdf

  Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $±(0, 1,...2^n)π/2^n$ and $±(0, 1,..., 3^n)π/3^n$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

  25 citations

• Optimal compression of quantum many-body time evolution operators into brickwall circuits

  Maurits S. J. Tepaske, Dominik Hahn, David J. Luitz

  SciPost Phys. 14, 073 (2023) · published 17 April 2023 | Toggle abstract · pdf

  Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the $S=1/2$ quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.

  25 citations

• Machine learning and quantum devices

  Florian Marquardt

  SciPost Phys. Lect. Notes 29 (2021) · published 31 May 2021 | Toggle abstract · pdf

  These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation, image classification, convolutional networks and autoencoders. The second part is about advanced techniques like reinforcement learning (for discovering control strategies), recurrent neural networks (for analyzing time traces), and Boltzmann machines (for learning probability distributions). In the third lecture, we discuss first recent applications to quantum physics, with an emphasis on quantum information processing machines. Finally, the fourth lecture is devoted to the promise of using quantum effects to accelerate machine learning.

  25 citations

• Front dynamics in the XY chain after local excitations

  Viktor Eisler, Florian Maislinger

  SciPost Phys. 8, 037 (2020) · published 6 March 2020 | Toggle abstract · pdf

  We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.

  25 citations

• Impurities in a one-dimensional Bose gas: the flow equation approach

  Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev

  SciPost Phys. 11, 008 (2021) · published 13 July 2021 | Toggle abstract · pdf

  A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

  25 citations

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections

  Salvatore D. Pace, Guilherme Delfino, Ho Tat Lam, Ömer M. Aksoy

  SciPost Phys. 18, 021 (2025) · published 17 January 2025 | Toggle abstract · pdf

  Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

  25 citations

• Towards explicit discrete holography: Aperiodic spin chains from hyperbolic tilings

  Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, Zhuo-Yu Xian

  SciPost Phys. 13, 103 (2022) · published 3 November 2022 | Toggle abstract · pdf

  We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic Poincaré disk, via an inflation rule that allows to construct the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains, whose sequences of couplings are obtained from the bulk inflation rule. We explicitly choose the aperiodic XXZ spin chain with spin 1/2 degrees of freedom as an example. The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. This can be regarded as discrete bulk reconstruction. Moreover we compute the entanglement entropy in this setup in two different ways: a discretization of the Ryu-Takayanagi formula and a generalization of the standard computation for the boundary aperiodic Hamiltonian. For both approaches, a logarithmic growth of the entanglement entropy in the subsystem size is identified. The coefficients, i.e. the effective central charges, depend on the bulk discretization parameters in both cases, albeit in a different way.

  25 citations

• Sparse sampling and tensor network representation of two-particle Green's functions

  Hiroshi Shinaoka, Dominique Geffroy, Markus Wallerberger, Junya Otsuki, Kazuyoshi Yoshimi, Emanuel Gull, Jan Kuneš

  SciPost Phys. 8, 012 (2020) · published 28 January 2020 | Toggle abstract · pdf

  Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green's functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green's functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.

  25 citations