Publications

Order by: publication date number of citations

• Statistical Floquet prethermalization of the Bose-Hubbard model

  Emanuele G. Dalla Torre, David Dentelski

  SciPost Phys. 11, 040 (2021) · published 24 August 2021 | Toggle abstract · pdf

  The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

  10 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.

  23 citations

• Entanglement entropy with Lifshitz fermions

  Dion Hartmann, Kevin Kavanagh, Stefan Vandoren

  SciPost Phys. 11, 031 (2021) · published 17 August 2021 | Toggle abstract · pdf

  We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent $z$. Remarkably, in the ground state the entanglement entropy vanishes for even values of $z$, whereas for odd values it is independent of $z$ and equal to the relativistic case with $z=1$. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of $z$ and $T$ which we plot using the lattice correlation method. The dependence on the even- or oddness of $z$ still shows for small temperatures, but is washed out for large temperatures or large values of $z$.

  8 citations

• Why space could be quantised on a different scale to matter

  Matthew J. Lake

  SciPost Phys. Proc. 4, 014 (2021) · published 13 August 2021 | Toggle abstract · pdf

  The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to $\hbar$. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics', namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, $\beta \ll \hbar$, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

  7 citations

• Position-dependent mass quantum systems and ADM formalism

  Davood Momeni

  SciPost Phys. Proc. 4, 009 (2021) · published 13 August 2021 | Toggle abstract · pdf

  The classical Einstein-Hilbert (EH) action for general relativity (GR) is shown to be formally analogous to the classical system with position-dependent mass (PDM) models. The analogy is developed and used to build the covariant classical Hamiltonian as well as defining an alternative phase portrait for GR. The set of associated Hamilton's equations in the phase space is presented as a first-order system dual to the Einstein field equations. Following the principles of quantum mechanics, I build a canonical theory for the classical general. A fully consistent quantum Hamiltonian for GR is constructed based on adopting a high dimensional phase space. It is observed that the functional wave equation is timeless. As a direct application, I present an alternative wave equation for quantum cosmology. In comparison to the standard Arnowitt-Deser-Misner(ADM) decomposition and quantum gravity proposals, I extended my analysis beyond the covariant regime when the metric is decomposed into the 3+1 dimensional ADM decomposition. I showed that an equal dimensional phase space can be obtained if one applies ADM decomposed metric.

  1 citation

• Flow equations for disordered Floquet systems

  Steven J. Thomson, Duarte Magano, Marco Schirò

  SciPost Phys. 11, 028 (2021) · published 10 August 2021 | Toggle abstract · pdf

  In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

  13 citations

• Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses

  Daniel Burgarth, Paolo Facchi, Martin Fraas, Robin Hillier

  SciPost Phys. 11, 027 (2021) · published 10 August 2021 | Toggle abstract · pdf

  Dynamical decoupling is the leading technique to remove unwanted interactions in a vast range of quantum systems through fast rotations. But what determines the time-scale of such rotations in order to achieve good decoupling? By providing an explicit counterexample of a qubit coupled to a charged particle and magnetic monopole, we show that such time-scales cannot be decided by the decay profile induced by the noise: even though the system shows a quadratic decay (a Zeno region revealing non-Markovian noise), it cannot be decoupled by periodic spin echo pulses, no matter how fast the rotations.

  9 citations

• Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

  Korbinian Kottmann, Philippe Corboz, Maciej Lewenstein, Antonio Acín

  SciPost Phys. 11, 025 (2021) · published 9 August 2021 | Toggle abstract · pdf

  We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improved by post-selecting ground-states based on their energy at the cost of contracting the tensor network once. Moreover, we show that the mantra of ``more training data leads to better results'' is not true for the learning task at hand and that, in principle, one training example suffices for this learning task. This puts the necessity of neural network optimizations for these learning tasks in question and we show that, at least for the model and data at hand, a simple geometric analysis suffices.

  10 citations

• Polynomial filter diagonalization of large Floquet unitary operators

  David J. Luitz

  SciPost Phys. 11, 021 (2021) · published 3 August 2021 | Toggle abstract · pdf

  Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size $L$ are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions $\geq 10^6$.

  11 citations

• Exact thermal properties of free-fermionic spin chains

  Michał Białończyk, Fernando Javier Gómez-Ruiz, Adolfo del Campo

  SciPost Phys. 11, 013 (2021) · published 15 July 2021 | Toggle abstract · pdf

  An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

  7 citations