Publications

Order by: publication date number of citations

• Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach

  Tatsuhiko N. Ikeda, Koki Chinzei, Masahiro Sato

  SciPost Phys. Core 4, 033 (2021) · published 24 December 2021 | Toggle abstract · pdf

  Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.

  24 citations

• QGOpt: Riemannian optimization for quantum technologies

  Ilia A. Luchnikov, Alexander Ryzhov, Sergey N. Filippov, Henni Ouerdane

  SciPost Phys. 10, 079 (2021) · published 30 March 2021 | Toggle abstract · pdf

  Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

  24 citations

• Towards explicit discrete holography: Aperiodic spin chains from hyperbolic tilings

  Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, Zhuo-Yu Xian

  SciPost Phys. 13, 103 (2022) · published 3 November 2022 | Toggle abstract · pdf

  We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic Poincaré disk, via an inflation rule that allows to construct the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains, whose sequences of couplings are obtained from the bulk inflation rule. We explicitly choose the aperiodic XXZ spin chain with spin 1/2 degrees of freedom as an example. The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. This can be regarded as discrete bulk reconstruction. Moreover we compute the entanglement entropy in this setup in two different ways: a discretization of the Ryu-Takayanagi formula and a generalization of the standard computation for the boundary aperiodic Hamiltonian. For both approaches, a logarithmic growth of the entanglement entropy in the subsystem size is identified. The coefficients, i.e. the effective central charges, depend on the bulk discretization parameters in both cases, albeit in a different way.

  24 citations

• DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

  P. Myles Eugenio, Ceren B. Dağ

  SciPost Phys. Core 3, 015 (2020) · published 9 December 2020 | Toggle abstract · pdf

  Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern$=\pm1$), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL's with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL's with the same magnetic field. In the first scenario -- which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene -- the opposite Chern LLL's are Kramer pairs, and thus there exists time-reversal symmetry ($\mathbb{Z}_2$). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry -- a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern $|++\cdots+>$ or all negative $|--\cdots->$. If instead, interactions are taken between electrons of like-Chern number, the ground state is an $SU(2)$ ferromagnet, with total spin pointing along an arbitrary direction, as with the $\nu=1$ spin-$\frac{1}{2}$ quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

  24 citations

• Dark matter in anomaly-free gauge extensions

  Martin Bauer, Sascha Diefenbacher, Tilman Plehn, Michael Russell, Daniel A. Camargo

  SciPost Phys. 5, 036 (2018) · published 19 October 2018 | Toggle abstract · pdf

  A consistent model for vector mediators to dark matter needs to be anomaly-free and include a scalar mode from mass generation. For the leading U(1) extensions we review the structure and constraints, including kinetic mixing at loop level. The thermal relic density suggests that the vector and scalar masses are similar. For the LHC we combine a $Z'$ shape analysis with mono-jets. For the latter, we find that a shape analysis offers significant improvement over existing cut-and-count approaches. Direct detection limits strongly constrain the kinetic mixing angle and we propose a $\ell^+\ell^- E_T$ search strategy based on the scalar mediator.

  24 citations

• Amorphous topological phases protected by continuous rotation symmetry

  Helene Spring, Anton R. Akhmerov, Daniel Varjas

  SciPost Phys. 11, 022 (2021) · published 5 August 2021 | Toggle abstract · pdf

  Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. While the local disorder caused by the amorphous structure weakens the topological protection, we demonstrate that the edge remains protected from localization. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

  24 citations

• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification

  Matteo Brunelli, Clara C. Wanjura, Andreas Nunnenkamp

  SciPost Phys. 15, 173 (2023) · published 19 October 2023 | Toggle abstract · pdf

  Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and extreme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary correspondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and without symmetries. We obtain the desired NH Hamiltonian from the mean-field evolution of driven-dissipative cavity arrays, in which NH terms-in the form of non-reciprocal hopping amplitudes, gain and loss-are explicitly modeled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the definition of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamiltonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value $\nu$ of the topological invariant defined in the bulk corresponds to $\vert \nu\vert$ singular vectors exponentially localized at the system edge under open boundary conditions, in which the sign of $\nu$ determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.

  24 citations

• Kibble–Zurek mechanism in the Ising Field Theory

  Kristóf Hódsági, Marton Kormos

  SciPost Phys. 9, 055 (2020) · published 20 October 2020 | Toggle abstract · pdf

  The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

  24 citations

• Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption

  Wei Chen, Gero von Gersdorff

  SciPost Phys. Core 5, 040 (2022) · published 16 August 2022 | Toggle abstract · pdf

  The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting point, we generalize these concepts by introducing dressed Berry curvature and quantum metric at finite temperature, in which the effect of many-body interactions can be included perturbatively. These quantities are extracted from the charge polarization susceptibility caused by linearly or circularly polarized electric fields, whose spectral functions can be measured from momentum-resolved exciton or infrared absorption rate. As a concrete example, we investigate Chern insulators in the presence of impurity scattering, whose results suggest that the quantum geometric properties are protected by the energy gap against many-body interactions.

  24 citations

• Information geometry in quantum field theory: lessons from simple examples

  Johanna Erdmenger, Kevin T. Grosvenor, Ro Jefferson

  SciPost Phys. 8, 073 (2020) · published 6 May 2020 | Toggle abstract · pdf

  Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By studying their Fisher metrics, we derive some general lessons that may have important implications for the application of information geometry in holography. We begin by demonstrating that the symmetries of the physical theory under study play a strong role in the resulting geometry, and that the appearance of an AdS metric is a relatively general feature. We then investigate what information the Fisher metric retains about the physics of the underlying theory by studying the geometry for both the classical 2d Ising model and the corresponding 1d free fermion theory, and find that the curvature diverges precisely at the phase transition on both sides. We discuss the differences that result from placing a metric on the space of theories vs. states, using the example of coherent free fermion states. We compare the latter to the metric on the space of coherent free boson states and show that in both cases the metric is determined by the symmetries of the corresponding density matrix. We also clarify some misconceptions in the literature pertaining to different notions of flatness associated to metric and non-metric connections, with implications for how one interprets the curvature of the geometry. Our results indicate that in general, caution is needed when connecting the AdS geometry arising from certain models with the AdS/CFT correspondence, and seek to provide a useful collection of guidelines for future progress in this exciting area.

  24 citations