Publications

Order by: publication date number of citations

• Chiral magnetism: a geometric perspective

  Daniel Hill, Valeriy Slastikov, Oleg Tchernyshyov

  SciPost Phys. 10, 078 (2021) · published 29 March 2021 | Toggle abstract · pdf

  We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

  12 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.

  11 citations

• Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta$_2$NiSe$_5$

  Satoshi Ejima, Florian Lange, Holger Fehske

  SciPost Phys. 10, 077 (2021) · published 26 March 2021 | Toggle abstract · pdf

  Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta$_2$NiSe$_5$. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta$_2$NiSe$_5$ the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta $k\simeq\pm k_{\rm F}$, which suggests that Ta$_2$NiSe$_5$ develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.

  9 citations

• Schur sector of Argyres-Douglas theory and $W$-algebra

  Dan Xie, Wenbin Yan

  SciPost Phys. 10, 080 (2021) · published 30 March 2021 | Toggle abstract · pdf

  We study the Schur index, the Zhu's $C_2$ algebra, and the Macdonald index of a four dimensional $\mathcal{N}=2$ Argyres-Douglas (AD) theories from the structure of the associated two dimensional $W$-algebra. The Schur index is derived from the vacuum character of the corresponding $W$-algebra and can be rewritten in a very simple form, which can be easily used to verify properties like level-rank dualities, collapsing levels, and S-duality conjectures. The Zhu's $C_2$ algebra can be regarded as a ring associated with the Schur sector, and a surprising connection between certain Zhu's $C_2$ algebra and the Jacobi algebra of a hypersurface singularity is discovered. Finally, the Macdonald index is computed from the Kazhdan filtration of the $W$-algebra.

  9 citations

• Local optimization on pure Gaussian state manifolds

  Bennet Windt, Alexander Jahn, Jens Eisert, Lucas Hackl

  SciPost Phys. 10, 066 (2021) · published 11 March 2021 | Toggle abstract · pdf

  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

  8 citations

• Supervised learning of few dirty bosons with variable particle number

  Pere Mujal, Àlex Martínez Miguel, Artur Polls, Bruno Juliá-Díaz, Sebastiano Pilati

  SciPost Phys. 10, 073 (2021) · published 24 March 2021 | Toggle abstract · pdf

  We investigate the supervised machine learning of few interacting bosons in optical speckle disorder via artificial neural networks. The learning curve shows an approximately universal power-law scaling for different particle numbers and for different interaction strengths. We introduce a network architecture that can be trained and tested on heterogeneous datasets including different particle numbers. This network provides accurate predictions for all system sizes included in the training set and, by design, is suitable to attempt extrapolations to (computationally challenging) larger sizes. Notably, a novel transfer-learning strategy is implemented, whereby the learning of the larger systems is substantially accelerated and made consistently accurate by including in the training set many small-size instances.

  7 citations

• Phonon redshift and Hubble friction in an expanding BEC

  Stephen Eckel, Ted Jacobson

  SciPost Phys. 10, 064 (2021) · published 11 March 2021 | Toggle abstract · pdf

  We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.

  7 citations

• Symmetries versus the spectrum of $ J\bar T$-deformed CFTs

  Monica Guica

  SciPost Phys. 10, 065 (2021) · published 11 March 2021 | Toggle abstract · pdf

  It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar T$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.

  6 citations

• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations

• Signatures of folded branches in the scanning gate microscopy of ballistic electronic cavities

  Keith R. Fratus, Camille Le Calonnec, Rodolfo A. Jalabert, Guillaume Weick, Dietmar Weinmann

  SciPost Phys. 10, 069 (2021) · published 17 March 2021 | Toggle abstract · pdf

  We demonstrate the emergence of classical features in electronic quantum transport for the scanning gate microscopy response in a cavity defined by a quantum point contact and a micron-sized circular reflector. The branches in electronic flow characteristic of a quantum point contact opening on a two-dimensional electron gas with weak disorder are folded by the reflector, yielding a complex spatial pattern. Considering the deflection of classical trajectories by the scanning gate tip allows to establish simple relationships of the scanning pattern, which are in agreement with recent experimental findings.

  4 citations