Publications

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• 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.

  16 citations

• Phase-space methods for simulating the dissipative many-body dynamics of collective spin systems

  Julian Huber, Peter Kirton, Peter Rabl

  SciPost Phys. 10, 045 (2021) · published 22 February 2021 | Toggle abstract · pdf

  We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

  16 citations

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

  Jean Michel Maillet, Giuliano Niccoli, Baptiste Pezelier

  SciPost Phys. 2, 009 (2017) · published 28 February 2017 | Toggle abstract · pdf

  We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions. Moreover, we prove an equivalent characterization as the set of solutions to a Baxter's like T-Q functional equation and rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form. In order to explain our method in a simple case, the present paper is restricted to representations containing one constraint on the boundary parameters and on the parameters of the Bazhanov-Stroganov Lax operator. In a next article, some more technical tools (like Baxter's gauge transformations) will be introduced to extend our approach to general integrable boundary conditions.

  16 citations

• Infinite pseudo-conformal symmetries of classical $T \bar T$, $J \bar T $ and $J T_a$ - deformed CFTs

  Monica Guica, Ruben Monten

  SciPost Phys. 11, 078 (2021) · published 18 October 2021 | Toggle abstract · pdf

  We show that $T \bar T, J \bar T$ and $J T_a$ - deformed classical CFTs possess an infinite set of symmetries that take the form of a field-dependent generalization of two-dimensional conformal transformations. If, in addition, the seed CFTs possess an affine $U(1)$ symmetry, we show that it also survives in the deformed theories, again in a field-dependent form. These symmetries can be understood as the infinitely-extended conformal and $U(1)$ symmetries of the underlying two-dimensional CFT, seen through the prism of the "dynamical coordinates" that characterise each of these deformations. We also compute the Poisson bracket algebra of the associated conserved charges, using the Hamiltonian formalism. In the case of the $J \bar T$ and $J T_a$ deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the $T \bar T$ deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra.

  16 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.

  16 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.

  16 citations

• $\mathcal{N}=2$ minimal models: A holographic needle in a symmetric orbifold haystack

  Alexandre Belin, Nathan Benjamin, Alejandra Castro, Sarah M. Harrison, Christoph A. Keller

  SciPost Phys. 8, 084 (2020) · published 3 June 2020 | Toggle abstract · pdf

  We explore large-$N$ symmetric orbifolds of the $\mathcal N=2$ minimal models, and find evidence that their moduli spaces each contain a supergravity point. We identify single-trace exactly marginal operators that deform them away from the symmetric orbifold locus. We also show that their elliptic genera exhibit slow growth consistent with supergravity spectra in AdS$_3$. We thus propose an infinite family of new holographic CFTs.

  16 citations

• Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands

  Jorrit Kruthoff, Raghu Mahajan, Chitraang Murdia

  SciPost Phys. 11, 063 (2021) · published 21 September 2021 | Toggle abstract · pdf

  We study the entanglement entropy of free fermions in 2d in the presence of a partially transmitting interface that splits Minkowski space into two half-spaces. We focus on the case of a single interval that straddles the defect, and compute its entanglement entropy in three limits: Perturbing away from the fully transmitting and fully reflecting cases, and perturbing in the amount of asymmetry of the interval about the defect. Using these results within the setup of the Poincaré patch of AdS$_2$ statically coupled to a zero temperature flat space bath, we calculate the effect of a partially transmitting AdS$_2$ boundary on the location of the entanglement island region. The partially transmitting boundary is a toy model for black hole graybody factors. Our results indicate that the entanglement island region behaves in a monotonic fashion as a function of the transmission/reflection coefficient at the interface.

  16 citations

• Weak integrability breaking and level spacing distribution

  D. Szász-Schagrin, B. Pozsgay, G. Takács

  SciPost Phys. 11, 037 (2021) · published 23 August 2021 | Toggle abstract · pdf

  Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.

  16 citations

• Linearized regime of the generalized hydrodynamics with diffusion

  Miłosz Panfil, Jacek Pawełczyk

  SciPost Phys. Core 1, 002 (2019) · published 22 November 2019 | Toggle abstract · pdf

  We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially. We exhibit some general features of the resulting dynamics, among them, we highlight the difference between the ballistic and diffusive evolution. The first one governs a spatial scrambling, the second, a scrambling of the quasi-particles content. We also go one step beyond the linear regime and discuss the evolution of the zero momentum mode that does not evolve in the linear regime.

  16 citations