Publications

Order by: publication date number of citations

• The non-rational limit of D-series minimal models

  Sylvain Ribault

  SciPost Phys. Core 3, 002 (2020) · published 31 July 2020 | Toggle abstract · pdf

  We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty, 1)$. We find that the limit theory's diagonal three-point structure constant differs from that of Liouville theory by a distribution factor, which is given by a divergent Verlinde formula. Nevertheless, correlation functions that involve both non-diagonal and diagonal fields are smooth functions of the diagonal fields' conformal dimensions. The limit theory is a non-trivial example of a non-diagonal, non-rational, solved two-dimensional conformal field theory.

• 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.

  15 citations

• Plasmons in holographic graphene

  Ulf Gran, Marcus Tornsö, Tobias Zingg

  SciPost Phys. 8, 093 (2020) · published 25 June 2020 | Toggle abstract · pdf

  We demonstrate how self-sourced collective modes - of which the plasmon is a prominent example due to its relevance in modern technological applications - are identified in strongly correlated systems described by holographic Maxwell theories. The characteristic $\omega \propto \sqrt{k}$ plasmon dispersion for 2D materials, such as graphene, naturally emerges from this formalism. We also demonstrate this by constructing the first holographic model containing this feature. This provides new insight into modeling such systems from a holographic point of view, bottom-up and top-down alike. Beyond that, this method provides a general framework to compute the dynamical charge response of strange metals, which has recently become experimentally accessible due to the novel technique of momentum-resolved electron energy-loss spectroscopy (M-EELS). This framework therefore opens up the exciting possibility of testing holographic models for strange metals against actual experimental data.

  5 citations

• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits

  Bruno Bertini, Pavel Kos, Tomaz Prosen

  SciPost Phys. 8, 068 (2020) · published 28 April 2020 | Toggle abstract · pdf

  We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.

  35 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.

  69 citations

• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

  Márton Mestyán, Vincenzo Alba

  SciPost Phys. 8, 055 (2020) · published 9 April 2020 | Toggle abstract · pdf

  We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb--Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the {\it full-time} dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

  14 citations

• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

  Oleksandr Gamayun, Oleg Lychkovskiy, Mikhail B. Zvonarev

  SciPost Phys. 8, 053 (2020) · published 7 April 2020 | Toggle abstract · pdf

  We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas δ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

  16 citations

• Entangled states of dipolar bosons generated in a triple-well potential

  Arlei P. Tonel, Leandro H. Ymai, Karin Wittmann W., Angela Foerster, Jon Links

  SciPost Phys. Core 2, 003 (2020) · published 11 March 2020 | Toggle abstract · pdf

  We study the generation of entangled states using a device constructed from dipolar bosons confined to a triple-well potential. Dipolar bosons possess controllable, long-range interactions. This property permits specific choices to be made for the coupling parameters, such that the system is integrable. Integrability assists in the analysis of the system via an effective Hamiltonian constructed through a conserved operator. Through computations of fidelity we establish that this approach, to study the time-evolution of the entanglement for a class of non-entangled initial states, yields accurate approximations given by analytic formulae.

  10 citations

• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

  György Z. Fehér, Balázs Pozsgay

  SciPost Phys. 8, 034 (2020) · published 3 March 2020 | Toggle abstract · pdf

  The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable lattice models solvable by the nested Bethe Ansatz, with group symmetry $SU(N)$, $N\ge 3$. In these models the Bethe Ansatz involves various types of Bethe rapidities corresponding to the "nesting" procedure, describing the internal degrees of freedom for the excitations. We show that a complete set of charges for the GGE can be obtained from the known fusion hierarchy of transfer matrices. The resulting charges are quasi-local in a certain regime in rapidity space, and they completely fix the rapidity distributions of each string type from each nesting level.

  5 citations

• Algebraic structure of classical integrability for complex sine-Gordon

  Jean Avan, Luc Frappat, Eric Ragoucy

  SciPost Phys. 8, 033 (2020) · published 2 March 2020 | Toggle abstract · pdf

  The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.

  1 citation