Publications

Order by: publication date number of citations

• Comments on abelian Higgs models and persistent order

  Zohar Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou

  SciPost Phys. 6, 003 (2019) · published 9 January 2019 | Toggle abstract · pdf

  A natural question about Quantum Field Theory is whether there is a deformation to a trivial gapped phase. If the underlying theory has an anomaly, then symmetric deformations can never lead to a trivial phase. We discuss such discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We emphasize the role of charge conjugation symmetry in these anomalies; for example, we obtain nontrivial constraints on the degrees of freedom that live on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions. In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the Abelian Higgs model is dual to the Ising model. We also study variations of the Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical particle of unit charge. These models have a center symmetry and additional discrete anomalies. In the absence of a dynamical unit charge particle, the Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These models without a unit charge particle exhibit a remarkably persistent order: we prove that the system cannot be disordered by either quantum or thermal fluctuations. Equivalently, when these theories are studied on a circle, no matter how small or large the circle is, the ground state is non-trivial.

  111 citations

• Field theories with a vector global symmetry

  Nathan Seiberg

  SciPost Phys. 8, 050 (2020) · published 3 April 2020 | Toggle abstract · pdf

  Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.

  111 citations

• Phase transitions in the early universe

  Mark Hindmarsh, Marvin Lüben, Johannes Lumma, Martin Pauly

  SciPost Phys. Lect. Notes 24 (2021) · published 15 February 2021 | Toggle abstract · pdf

  These lecture notes are based on a course given by Mark Hindmarsh at the 24th Saalburg Summer School 2018 and written up by Marvin L\"uben, Johannes Lumma and Martin Pauly. The aim is to provide the necessary basics to understand first-order phase transitions in the early universe, to outline how they leave imprints in gravitational waves, and advertise how those gravitational waves could be detected in the future. A first-order phase transition at the electroweak scale is a prediction of many theories beyond the Standard Model, and is also motivated as an ingredient of some theories attempting to provide an explanation for the matter-antimatter asymmetry in our Universe. Starting from bosonic and fermionic statistics, we derive Boltzmann's equation and generalise to a fluid of particles with field dependent mass. We introduce the thermal effective potential for the field in its lowest order approximation, discuss the transition to the Higgs phase in the Standard Model and beyond, and compute the probability for the field to cross a potential barrier. After these preliminaries, we provide a hydrodynamical description of first-order phase transitions as it is appropriate for describing the early Universe. We thereby discuss the key quantities characterising a phase transition, and how they are imprinted in the gravitational wave power spectrum that might be detectable by the space-based gravitational wave detector LISA in the 2030s.

  106 citations

• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits

  Bruno Bertini, Pavel Kos, Tomaz Prosen

  SciPost Phys. 8, 067 (2020) · published 28 April 2020 | Toggle abstract · pdf

  The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of "completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a "phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.

  102 citations

• Efficient variational simulation of non-trivial quantum states

  Wen Wei Ho, Timothy H. Hsieh

  SciPost Phys. 6, 029 (2019) · published 7 March 2019 | Toggle abstract · pdf

  We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with $L$ variational parameters and physical runtimes $T$ that scale linearly with the system size $L$. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational ans\"atze as good descriptions of non-trivial states of matter.

  101 citations

• $T\bar T$ and the mirage of a bulk cutoff

  Monica Guica, Ruben Monten

  SciPost Phys. 10, 024 (2021) · published 1 February 2021 | Toggle abstract · pdf

  We use the variational principle approach to derive the large $N$ holographic dictionary for two-dimensional $T\bar T$-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial "bulk cutoff" is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

  100 citations

• Shift-invert diagonalization of large many-body localizing spin chains

  Francesca Pietracaprina, Nicolas Macé, David J. Luitz, Fabien Alet

  SciPost Phys. 5, 045 (2018) · published 6 November 2018 | Toggle abstract · pdf

  We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to $L=26$. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

  99 citations

• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

  Pietro Silvi, Ferdinand Tschirsich, Matthias Gerster, Johannes Jünemann, Daniel Jaschke, Matteo Rizzi, Simone Montangero

  SciPost Phys. Lect. Notes 8 (2019) · published 18 March 2019 | Toggle abstract · pdf

  We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.

  97 citations

• A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants

  Andreas Karch, David Tong, Carl Turner

  SciPost Phys. 7, 007 (2019) · published 10 July 2019 | Toggle abstract · pdf

  We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant $c=1$ CFTs that depend on a background spin structure.

  94 citations

• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

  Clay Córdova, Po-Shen Hsin, Nathan Seiberg

  SciPost Phys. 4, 021 (2018) · published 29 April 2018 | Toggle abstract · pdf

  We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for $SO(N)_{K}$ Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for $SO(N)$ to other global forms of the gauge group.

  94 citations