Publications

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• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

  Claudius Hubig, Annabelle Bohrdt, Michael Knap, Fabian Grusdt, J. Ignacio Cirac

  SciPost Phys. 8, 021 (2020) · published 6 February 2020 | Toggle abstract · pdf

  Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

  31 citations

• Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation

  Jing Li, Ivan Duchemin, Xavier Blase, Valerio Olevano

  SciPost Phys. 8, 020 (2020) · published 5 February 2020 | Toggle abstract · pdf

  Since the '30s the interatomic potential of the beryllium dimer Be$_2$ has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be$_2$ along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be$_2$ interatomic potential using the GW approximation and the Bethe-Salpeter equation (BSE). The ground-state correlation energy is calculated by the trace formula with checks against the adiabatic-connection fluctuation-dissipation theorem formula. We show that inclusion of GW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GW approximation, our calculation is in surprising agreement with the most accurate theories and with experiment. It even reproduces an experimentally observed flattening of the interatomic potential due to a delicate correlations balance from a competition between covalent and van der Waals bonding.

  12 citations

• The representation theory of seam algebras

  Alexis Langlois-Rémillard, Yvan Saint-Aubin

  SciPost Phys. 8, 019 (2020) · published 5 February 2020 | Toggle abstract · pdf

  The boundary seam algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Cramp\'e and Poulain d'Andecy.

  3 citations

• Lorentz symmetry fractionalization and dualities in (2+1)d

  Po-Shen Hsin, Shu-Heng Shao

  SciPost Phys. 8, 018 (2020) · published 4 February 2020 | Toggle abstract · pdf

  We discuss symmetry fractionalization of the Lorentz group in (2+1)d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous $\mathbb{Z}_2$ one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.

  22 citations

• Ground-state energy of a Richardson-Gaudin integrable BCS model

  Yibing Shen, Phillip S. Isaac, Jon Links

  SciPost Phys. Core 2, 001 (2020) · published 4 February 2020 | Toggle abstract · pdf

  We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

  4 citations

• Connecting quasinormal modes and heat kernels in 1-loop determinants

  Cynthia Keeler, Victoria L. Martin, Andrew Svesko

  SciPost Phys. 8, 017 (2020) · published 3 February 2020 | Toggle abstract · pdf

  We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

  9 citations

• Current operators in integrable spin chains: lessons from long range deformations

  Balázs Pozsgay

  SciPost Phys. 8, 016 (2020) · published 3 February 2020 | Toggle abstract · pdf

  We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU(3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.

  46 citations

• On gauging finite subgroups

  Yuji Tachikawa

  SciPost Phys. 8, 015 (2020) · published 31 January 2020 | Toggle abstract · pdf

  We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup $A$ of a $\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that the symmetry of the gauged theory can be i) a direct product of $G=\Gamma/A$ and a higher-form symmetry $\hat A$ with a mixed anomaly, where $\hat A$ is the Pontryagin dual of $A$; ii) an extension of the ordinary symmetry group $G$ by the higher-form symmetry $\hat A$; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the $H^3(G,\hat A)$ symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

  157 citations

• Rank $Q$ E-string on a torus with flux

  Sara Pasquetti, Shlomo S. Razamat, Matteo Sacchi, Gabi Zafrir

  SciPost Phys. 8, 014 (2020) · published 29 January 2020 | Toggle abstract · pdf

  We discuss compactifications of rank $Q$ E-string theory on a torus with fluxes for abelian subgroups of the $E_8$ global symmetry of the $6d$ SCFT. We argue that the theories corresponding to such tori are built from a simple model we denote as $E[USp(2Q)]$. This model has a variety of non trivial properties. In particular the global symmetry is $USp(2Q)\times USp(2Q)\times U(1)^2$ with one of the two $USp(2Q)$ symmetries emerging in the IR as an enhancement of an $SU(2)^Q$ symmetry of the UV Lagrangian. The $E[USp(2Q)]$ model after dimensional reduction to $3d$ and a subsequent Coulomb branch flow is closely related to the familiar $3d$ $T[SU(Q)]$ theory, the model residing on an S-duality domain wall of $4d$ $\mathcal{N}=4$ $SU(Q)$ SYM. Gluing the $E[USp(2Q)]$ models by gauging the $USp(2Q)$ symmetries with proper admixtures of chiral superfields gives rise to systematic constructions of many examples of $4d$ theories with emergent IR symmetries. We support our claims by various checks involving computations of anomalies and supersymmetric partition functions. Many of the needed identities satisfied by the supersymmetric indices follow directly from recent mathematical results obtained by E. Rains.

  41 citations

• Time-resolved electrical detection of chiral edge vortex braiding

  İnanç Adagideli, Fabian Hassler, Aurélien Grabsch, Michał Pacholski, Carlo W. J. Beenakker

  SciPost Phys. 8, 013 (2020) · published 29 January 2020 | Toggle abstract · pdf

  A $\boldsymbol{2\pi}$ phase shift across a Josephson junction in a topological superconductor injects vortices into the chiral edge modes at opposite ends of the junction. When two vortices are fused they transfer charge into a metal contact. We calculate the time dependent current profile for the fusion process, which consists of $\boldsymbol{\pm e/2}$ charge pulses that flip sign if the world lines of the vortices are braided prior to the fusion. This is an electrical signature of the non-Abelian exchange of Majorana zero-modes.

  13 citations