Publications

Order by: publication date number of citations

• Boundary RG flows for fermions and the mod 2 anomaly

  Philip Boyle Smith, David Tong

  SciPost Phys. 10, 010 (2021) · published 19 January 2021 | Toggle abstract · pdf

  Boundary conditions for Majorana fermions in d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge, $g$. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by $g^2_{IR} / g^2_{UV} = {\rm dim}\,({\cal O})$, the dimension of the perturbing boundary operator. Any relevant operator necessarily has ${\rm dim}({\cal O}) < 1$, ensuring that the central charge decreases in accord with the g-theorem.

  9 citations

• Tagging Jets in Invisible Higgs Searches

  Anke Biekoetter, Fabian Keilbach, Rhea Moutafis, Tilman Plehn, Jennifer M. Thompson

  SciPost Phys. 4, 035 (2018) · published 22 June 2018 | Toggle abstract · pdf

  Searches for invisible Higgs decays in weak boson fusion are a well-known laboratory for jets and QCD studies. We present a series of results on tagging jets and central jet activity. First, precision analyses of the central jet activity require full control of single top production in some analyses. Second, the rate dependence on the size of the tagging jets is not limited to weak boson fusion. For the first time, we show how subjet information on the tagging jets and on the additional jet activity can be used to extract the Higgs signal. The additional observables relieve some of the pressure on other, critical observables. Finally, we compare the performance of weak boson fusion and associated Higgs production.

  9 citations

• Solving 3d gravity with Virasoro TQFT

  Scott Collier, Lorenz Eberhardt, Mengyang Zhang

  SciPost Phys. 15, 151 (2023) · published 11 October 2023 | Toggle abstract · pdf

  We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as "Virasoro TQFT". This TQFT is similar, but importantly not equivalent, to SL(2, $\mathbb{R}$) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, $\mathbb{R}$) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

  9 citations

• Quantum approximate optimization for hard problems in linear algebra

  Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco

  SciPost Phys. Core 4, 031 (2021) · published 30 November 2021 | Toggle abstract · pdf

  The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.

  9 citations

• Pivot Hamiltonians as generators of symmetry and entanglement

  Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen

  SciPost Phys. 14, 012 (2023) · published 2 February 2023 | Toggle abstract · pdf

  It is well-known that symmetry-protected topological (SPT) phases can be obtained from the trivial phase by an entangler, a finite-depth unitary operator $U$. Here, we consider obtaining the entangler from a local 'pivot' Hamiltonian $H_\text{pivot}$ such that $U = e^{i\pi H_\text{pivot}}$. This perspective of Hamiltonians pivoting between the trivial and SPT phase opens up two new directions: (i) Since SPT Hamiltonians and entanglers are now on the same footing, can we iterate this process to create other interesting states? (ii) Since entanglers are known to arise as discrete symmetries at SPT transitions, under what conditions can this be enhanced to $U(1)$ pivot symmetry generated by $H_\text{pivot}$? In this work we explore both of these questions. With regard to the first, we give examples of a rich web of dualities obtained by iteratively using an SPT model as a pivot to generate the next one. For the second question, we derive a simple criterion for when the direct interpolation between the trivial and SPT Hamiltonian has a $U(1)$ pivot symmetry. We illustrate this in a variety of examples, assuming various forms for $H_\text{pivot}$, including the Ising chain, and the toric code Hamiltonian. A remarkable property of such a $U(1)$ pivot symmetry is that it shares a mutual anomaly with the symmetry protecting the nearby SPT phase. We discuss how such anomalous and non-onsite $U(1)$ symmetries explain the exotic phase diagrams that can appear, including an SPT multicritical point where the gapless ground state is given by the fixed-point toric code state.

  9 citations

• Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

  Xhek Turkeshi, Marcello Dalmonte

  SciPost Phys. 8, 042 (2020) · published 16 March 2020 | Toggle abstract · pdf

  Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.

  9 citations

• Cavity and replica methods for the spectral density of sparse symmetric random matrices

  Vito A R Susca, Pierpaolo Vivo, Reimer Kühn

  SciPost Phys. Lect. Notes 33 (2021) · published 10 August 2021 | Toggle abstract · pdf

  We review the problem of how to compute the spectral density of sparse symmetric random matrices, i.e. weighted adjacency matrices of undirected graphs. Starting from the Edwards-Jones formula, we illustrate the milestones of this line of research, including the pioneering work of Bray and Rodgers using replicas. We focus first on the cavity method, showing that it quickly provides the correct recursion equations both for single instances and at the ensemble level. We also describe an alternative replica solution that proves to be equivalent to the cavity method. Both the cavity and the replica derivations allow us to obtain the spectral density via the solution of an integral equation for an auxiliary probability density function. We show that this equation can be solved using a stochastic population dynamics algorithm, and we provide its implementation. In this formalism, the spectral density is naturally written in terms of a superposition of local contributions from nodes of given degree, whose role is thoroughly elucidated. This paper does not contain original material, but rather gives a pedagogical overview of the topic. It is indeed addressed to students and researchers who consider entering the field. Both the theoretical tools and the numerical algorithms are discussed in detail, highlighting conceptual subtleties and practical aspects.

  9 citations

• Gate-induced decoupling of surface and bulk state properties in selectively-deposited Bi$_2$Te$_3$ nanoribbons

  Daniel Rosenbach, Kristof Moors, Abdur R. Jalil, Jonas Kölzer, Erik Zimmermann, Jürgen Schubert, Soraya Karimzadah, Gregor Mussler, Peter Schüffelgen, Detlev Grützmacher, Hans Lüth, Thomas Schäpers

  SciPost Phys. Core 5, 017 (2022) · published 30 March 2022 | Toggle abstract · pdf

  Three-dimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasi-one-dimensional TI nanoribbon structures the wave function of surface charges extends phase-coherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spin-momentum locking results in a Berry phase offset of $\pi$ of self-interfering charge carriers an energy gap within the surface state dispersion appears and all states become spin-degenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi$_2$Te$_3$ TI micro- and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. While in wide microribbon devices the field effect mainly changes the amount of bulk charges close to the top surface we identify coherent transverse surface states along the perimeter of the nanoribbon devices responding to a change in top gate potential. We quantify the energetic spacing in between these quantized transverse subbands by using an electrostatic model that treats an initial difference in charge carrier densities on the top and bottom surface as well as remaining bulk charges. In the gate voltage dependent transconductance we find oscillations that change their relative phase by $\pi$ at half-integer values of the magnetic flux quantum applied coaxial to the nanoribbon, which is a signature for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices.

  9 citations

• Charge fluctuation entropy of Hawking radiation: A replica-free way to find large entropy

  Alexey Milekhin, Amirhossein Tajdini

  SciPost Phys. 14, 172 (2023) · published 28 June 2023 | Toggle abstract · pdf

  We study the fluctuation entropy for two-dimensional matter systems with an internal symmetry coupled to Jackiw-Teitelboim (JT) gravity joined to a Minkowski region. The fluctuation entropy is the Shannon entropy associated to probabilities of finding particular charge for a region. We first consider a case where the matter has a global symmetry. We find that the fluctuation entropy of Hawking radiation shows an unbounded growth and exceeds the entanglement entropy in presence of islands. This indicates that the global symmetry is violated. We then discuss the fluctuation entropy for matter coupled to a two-dimensional gauge field. We find a lower bound on the gauge coupling $g_0$ in order to avoid a similar issue. Also, we point out a few puzzles related to the island prescription in presence of a gauge symmetry.

  9 citations

• Anisotropic scaling of the two-dimensional Ising model I: the torus

  Hendrik Hobrecht, Alfred Hucht

  SciPost Phys. 7, 026 (2019) · published 2 September 2019 | Toggle abstract · pdf

  We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and - if present - the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

  9 citations