Publications

Order by: publication date number of citations

• Space-like dynamics in a reversible cellular automaton

  Katja Klobas, Tomaž Prosen

  SciPost Phys. Core 2, 010 (2020) · published 26 June 2020 | Toggle abstract · pdf

  In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

  17 citations

• Topological lattice models with constant Berry curvature

  Daniel Varjas, Ahmed Abouelkomsan, Kang Yang, Emil J. Bergholtz

  SciPost Phys. 12, 118 (2022) · published 6 April 2022 | Toggle abstract · pdf

  Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

  17 citations

• Gravitational waves from an axion-dark photon system: A lattice study

  Wolfram Ratzinger, Pedro Schwaller, Ben A. Stefanek

  SciPost Phys. 11, 001 (2021) · published 6 July 2021 | Toggle abstract · pdf

  In this work, we present a lattice study of an axion - dark photon system in the early Universe and show that the stochastic gravitational wave (GW) background produced by this system may be probed by future GW experiments across a vast range of frequencies. The numerical simulation on the lattice allows us to take into account non-linear backreaction effects and enables us to accurately predict the final relic abundance of the axion or axion-like particle (ALP) as well as its inhomogeneities, and gives a more precise prediction of the GW spectrum. Importantly, we find that the GW spectrum has more power at high momenta due to $2\rightarrow1$ processes. Furthermore, we find the degree of polarization of the peak of the GW spectrum depends on the ALP-dark photon coupling and that the polarization can be washed out or even flipped for large values thereof. In line with recent results in the literature, we find the ALP relic abundance may be suppressed by two orders of magnitude and discuss possible extensions of the model that expand the viable parameter space. Finally, we discuss the possibility to probe ultralight ALP dark matter via spectral distortions of the CMB.

  17 citations

• Charged quantum fields in AdS$_2$

  Dionysios Anninos, Diego M. Hofman, Jorrit Kruthoff

  SciPost Phys. 7, 054 (2019) · published 23 October 2019 | Toggle abstract · pdf

  We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an $SL(2,\mathbb{R})$ invariant AdS$_2$ geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS$_2$ boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we 'UV' complete AdS$_2$ by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the flux-carrying modes that resembles the standard flat space S-matrix. We relate various features displayed by the highly charged particles to the principal series representations of $SL(2,\mathbb{R})$. These representations are unitary and also appear for massive quantum fields in dS$_2$. Both fermionic and bosonic fields are studied. We find that the free charged massless fermion is exactly solvable for general background, providing an interesting arena for the problem at hand.

  17 citations

• Magnetism of magic-angle twisted bilayer graphene

  Javad Vahedi, Robert Peters, Ahmed Missaoui, Andreas Honecker, Guy Trambly de Laissardière

  SciPost Phys. 11, 083 (2021) · published 27 October 2021 | Toggle abstract · pdf

  We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called "magic angles" using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction $U$ that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effect is overestimated in the rescaled system, hinting at a complex interplay of flatness of the minibands close to the Fermi level and the spatial extent of the corresponding localized states. Our findings shed new light on perspectives for experimental realization of magnetic states in charge-neutral twisted bilayer graphene.

  17 citations

• Yang-Baxter and the Boost: splitting the difference

  Marius de Leeuw, Chiara Paletta, Anton Pribytok, Ana L. Retore, Paul Ryan

  SciPost Phys. 11, 069 (2021) · published 27 September 2021 | Toggle abstract · pdf

  In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16×16 solutions which exhibit su(2)+su(2) symmetry, which include the one-dimensional Hubbard model and the S-matrix of the AdS5 x S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

  17 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.

  17 citations

• Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

  Yin-Chen He, Junchen Rong, Ning Su

  SciPost Phys. 10, 115 (2021) · published 26 May 2021 | Toggle abstract · pdf

  It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of $O(N)$ vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough $N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$ Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. We further carry out dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$ deconfined phase transition. We find the kink disappears at around $d=2.7$ dimensions indicating the $SO(5)$ deconfined phase transition is weakly first order. The second interesting observation is, the $O(2)$ bootstrap bound does not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the $N=\infty$ limit, where the non-WF kink sits at $(\Delta_\phi, \Delta_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF CFTs originating from free boson at $N=\infty$.

  17 citations

• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

  Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino

  SciPost Phys. Core 4, 026 (2021) · published 7 October 2021 | Toggle abstract · pdf

  $Circuit~ Complexity$, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. $Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides $circuit~ complexity$, we use the $Out-of-Time~ Ordered~ correlation~ (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible, but an exponential rise can be seen in the $complexity$ once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC. Furthermore, from the $complexity$ computation obtained from both the cosmological models and also using the well known MSS bound on quantum Lyapunov exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at late time scale. Finally, we provide a rough estimation of the scrambling time in terms of the conformal time.

  17 citations

• Rank $Q$ E-string on spheres with flux

  Chiung Hwang, Shlomo S. Razamat, Evyatar Sabag, Matteo Sacchi

  SciPost Phys. 11, 044 (2021) · published 30 August 2021 | Toggle abstract · pdf

  We consider compactifications of rank $Q$ E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the $\mathrm{E}_8\times \mathrm{SU}(2)$ global symmetry group of the six dimensional theory. We first construct a simple Wess--Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of $\mathrm{E}_8$ leads to the S-confinement duality of the $\mathrm{USp}(2Q)$ gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an $\mathrm{SU}(2)_{\text{ISO}}$ symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the $\mathrm{SU}(2)_{\text{ISO}}$ in 4d and comparing them with the predicted anomalies from 6d.

  17 citations