Publications

Order by: publication date number of citations

• Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

  Luís F. Alves da Silva, Rodrigo A. Dourado, Miled H. Y. Moussa

  SciPost Phys. Core 5, 012 (2022) · published 14 March 2022 | Toggle abstract · pdf

  In this work we first propose a method for the derivation of a general continuous antilinear time-dependent (TD) symmetry operator I(t) for a TD non-Hermitian Hamiltonian H(t). Assuming H(t) to be simultaneously ρ(t)-pseudo-Hermitian and Ξ(t)-anti-pseudo-Hermitian, we also derive the antilinear symmetry I(t)=Ξ⁻¹(t)ρ(t), which retrieves an important result obtained by Mostafazadeh [J. Math, Phys. 43, 3944 (2002)] for the time-independent (TI) scenario. We apply our method for the derivaton of the symmetry associated with TD non-Hermitian linear and quadratic Hamiltonians. The computed TD symmetry operators for both cases are then particularized for their equivalent TI lHamiltonians and PT-symmetric restrictions. In the TI scenario we retrieve the well-known Bender-Berry-Mandilara result for the symmetry operator: I^{2k}=1 with k odd [J. Phys. A 35, L467 (2002)]. The results here derived allow us to propose a useful symmetry-metric relation for TD non-Hermitian Hamiltonians. From this relation the TD metric is automatically derived from the TD symmetry of the problem. Then, when placed in perspective with the antilinear symmetry I(t)=Ξ⁻¹(t)ρ(t), the symmetry-metric relation finally allow us to derive the Ξ(t)-anti-pseudo-Hermitian operator. Our results reinforce the prospects of going beyond PT-symmetric quantum mechanics making the field of pseudo-Hermiticity even more comprehensive and promising.

  1 citation

• Quantum enhanced metrology in the search for fundamental physical phenomena

  Konrad W. Lehnert

  SciPost Phys. Lect. Notes 40 (2022) · published 11 March 2022 | Toggle abstract · pdf

  These notes summarize lectures given at the 2019 Les Houches summer school on Quantum Information Machines. They describe and review an application of quantum metrology concepts to searches for ultralight dark matter. In particular, for ultralight dark matter that couples as a weak classical force to a laboratory harmonic oscillator, quantum squeezing benefits experiments in which the mass of the dark matter particle is unknown. This benefit is present even if the oscillatory dark matter signal is much more coherent than the harmonic oscillator that it couples to, as is the case for microwave frequency searches for dark matter axion particles.

  3 citations

• Relative entropic uncertainty relation for scalar quantum fields

  Stefan Floerchinger, Tobias Haas, Markus Schröfl

  SciPost Phys. 12, 089 (2022) · published 10 March 2022 | Toggle abstract · pdf

  Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum field theories. In this work, we overcome this difficulty by introducing the notion of a functional relative entropy and show that it has a meaningful field theory limit. We present the first entropic uncertainty relation for a scalar quantum field theory and exemplify its behavior by considering few particle excitations and the thermal state. Also, we show that the relation implies the multidimensional Heisenberg uncertainty relation.

  2 citations

• Circular Rosenzweig-Porter random matrix ensemble

  Wouter Buijsman, Yevgeny Bar Lev

  SciPost Phys. 12, 082 (2022) · published 3 March 2022 | Toggle abstract · pdf

  The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems. We propose a unitary (circular) analogue of this ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. We define this ensemble as the outcome of a Dyson Brownian motion process. We show numerical evidence that this ensemble shares some key statistical properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates.

  14 citations

• Local measures of entanglement in black holes and CFTs

  Andrew Rolph

  SciPost Phys. 12, 079 (2022) · published 1 March 2022 | Toggle abstract · pdf

  We study the structure and dynamics of entanglement in CFTs and black holes. We use a local entanglement measure, the entanglement contour, which is a spatial density function for von Neumann entropy with some additional properties. The entanglement contour can be calculated in many 1+1d condensed matter systems and simple models of black hole evaporation. We calculate the entanglement contour of a state excited by a splitting quench, and find universal results for the entanglement contours of low energy non-equilibrium states in 2d CFTs. We also calculate the contour of a non-gravitational bath coupled to an extremal AdS$_2$ black hole, and find that the contour only has finite support within the bath, due to an island phase transition. The particular entanglement contour proposal we use quantifies how well the bath's state can be reconstructed from its marginals, through its connection to conditional mutual information, and the vanishing contour is a reflection of the protection of bulk island regions against erasures of the boundary state.

  15 citations

• Devil's staircase of topological Peierls insulators and Peierls supersolids

  Titas Chanda, Daniel González-Cuadra, Maciej Lewenstein, Luca Tagliacozzo, Jakub Zakrzewski

  SciPost Phys. 12, 076 (2022) · published 25 February 2022 | Toggle abstract · pdf

  We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.

  7 citations

• Topological Frustration can modify the nature of a Quantum Phase Transition

  Vanja Marić, Gianpaolo Torre, Fabio Franchini, Salvatore Marco Giampaolo

  SciPost Phys. 12, 075 (2022) · published 24 February 2022 | Toggle abstract · pdf

  Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

  8 citations

• Polariton condensation into vortex states in the synthetic magnetic field of a strained honeycomb lattice

  Cristóbal Lledó, Iacopo Carusotto, Marzena H. Szymańska

  SciPost Phys. 12, 068 (2022) · published 18 February 2022 | Toggle abstract · pdf

  Photonic materials are a rapidly growing platform for studying condensed matter physics with light, where the exquisite control capability is allowing us to learn about the relation between microscopic dynamics and macroscopic properties. One of the most interesting aspects of condensed matter is the interplay between interactions and the effect of an external magnetic field or rotation, responsible for a plethora of rich phenomena---Hall physics and quantized vortex arrays. At first sight, however, these effects for photons seem vetoed: they do not interact with each other and they are immune to magnetic fields and rotations. Yet in specially devised structures these effects can be engineered. Here, we propose the use of a synthetic magnetic field induced by strain in a honeycomb lattice of resonators to create a non-equilibrium Bose-Einstein condensate of light-matter particles (polaritons) in a rotating state, without the actual need for external rotation nor reciprocity-breaking elements. We show that thanks to the competition between interactions, dissipation and a suitably designed incoherent pump, the condensate spontaneously becomes chiral by selecting a single Dirac valley of the honeycomb lattice, occupying the lowest Landau level and forming a vortex array. Our results offer a new platform where to study the exciting physics of arrays of quantized vortices with light and pave the way to explore the transition from a vortex-dominated phase to the photonic analogue of the fractional quantum Hall regime.

  5 citations

• Bloch oscillations and the lack of the decay of the false vacuum in a one-dimensional quantum spin chain

  O. Pomponio, M. A. Werner, G. Zarand, G. Takacs

  SciPost Phys. 12, 061 (2022) · published 15 February 2022 | Toggle abstract · pdf

  We consider the decay of the false vacuum, realised within a quantum quench into an anti-confining regime of the Ising spin chain with a magnetic field opposite to the initial magnetisation. Although the effective linear potential between the domain walls is repulsive, the time evolution of correlations still shows a suppression of the light cone and a reduction of vacuum decay. The suppressed decay is a lattice effect, and can be assigned to emergent Bloch oscillations.

  16 citations

• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

  Pavel A. Nosov, Ivan M. Khaymovich, Andrey Kudlis, Vladimir E. Kravtsov

  SciPost Phys. 12, 048 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

  5 citations