Publications

Order by: publication date number of citations

• Tangent-space methods for truncating uniform MPS

  Bram Vanhecke, Maarten Van Damme, Jutho Haegeman, Laurens Vanderstraeten, Frank Verstraete

  SciPost Phys. Core 4, 004 (2021) · published 19 February 2021 | Toggle abstract · pdf

  A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

  8 citations

• A study of collider signatures for two Higgs doublet models with a Pseudoscalar mediator to Dark Matter

  Jonathan M. Butterworth, Martin Habedank, Priscilla Pani, Andrius Vaitkus

  SciPost Phys. Core 4, 003 (2021) · published 18 February 2021 | Toggle abstract · pdf

  Two Higgs doublet models with an additional pseudoscalar particle coupling to the Standard Model and to a new stable, neutral particle, provide an attractive and fairly minimal route to solving the problem of Dark Matter. They have been the subject of several searches at the LHC. We study the impact of existing LHC measurements on such models, first in the benchmark regions addressed by searches and then after relaxing some of their assumptions and broadening the parameter ranges considered. In each case we study how the new parameters change the potentially visible signatures at the LHC, and identify which of these signatures should already have had a significant impact on existing measurements. This allows us to set some first constraints on a number of so far unstudied scenarios.

  10 citations

• The multi-faceted inverted harmonic oscillator: Chaos and complexity

  Arpan Bhattacharyya, Wissam Chemissany, S. Shajidul Haque, Jeff Murugan, Bin Yan

  SciPost Phys. Core 4, 002 (2021) · published 8 February 2021 | Toggle abstract · pdf

  The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.

  47 citations

• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension

  Mario Collura, Luca Dell'Anna, Timo Felser, Simone Montangero

  SciPost Phys. Core 4, 001 (2021) · published 2 February 2021 | Toggle abstract · pdf

  In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferromagnetic Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack of a detailed comparison of the expressiveness of these increasingly popular, variational ans\"atze.

  6 citations

• Euler-scale dynamical correlations in integrable systems with fluid motion

  Frederik S. Møller, Gabriele Perfetto, Benjamin Doyon, Jörg Schmiedmayer

  SciPost Phys. Core 3, 016 (2020) · published 22 December 2020 | Toggle abstract · pdf

  We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard-rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time-scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.

  22 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.

  18 citations

• Holonomic implementation of CNOT gate on topological Majorana qubits

  Alessio Calzona, Nicolas P. Bauer, Björn Trauzettel

  SciPost Phys. Core 3, 014 (2020) · published 3 December 2020 | Toggle abstract · pdf

  The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.

  5 citations

• Detect axial gauge fields with a calorimeter

  Matteo Baggioli, Maxim N. Chernodub, Karl Landsteiner, Maria A. H. Vozmediano

  SciPost Phys. Core 3, 013 (2020) · published 2 December 2020 | Toggle abstract · pdf

  Torsional strain in Weyl semimetals excites a unidirectional chiral density wave propagating in the direction of the torsional vector. This gapless excitation, named the chiral sound wave, is generated by a particular realization of the axial anomaly via the triple-axial (AAA) anomalous diagram. We show that the presence of the torsion-generated chiral sound leads to a linear behavior of the specific heat of a Weyl semimetal and to an enhancement of the thermal conductivty at experimentally accessible temperatures. We also demonstrate that such an elastic twist lowers the temperature of the sample, thus generating a new, anomalous type of elasto-calorific effect. Measurements of these thermodynamical effects will provide experimental verification of the exotic triple-axial anomaly as well as the reality of the elastic pseudomagnetic fields in Weyl semimetals.

  4 citations

• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

  Tommaso Micallo, Vittorio Vitale, Marcello Dalmonte, Pierre Fromholz

  SciPost Phys. Core 3, 012 (2020) · published 1 December 2020 | Toggle abstract · pdf

  We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants.

  17 citations

• Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

  Iman Mahyaeh, Jurriaan Wouters, Dirk Schuricht

  SciPost Phys. Core 3, 011 (2020) · published 12 November 2020 | Toggle abstract · pdf

  We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

  4 citations