SciPost: SciPost Physics Core: issue detail

SciPost Physics Core

SciPost Physics Core Vol. 4 issue 1 (January - March 2021)

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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 | · 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.
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 | · 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.
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 | · 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.
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 | · 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.
On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

Dainius Kilda, Alberto Biella, Marco Schirò, Rosario Fazio, Jonathan Keeling

SciPost Phys. Core 4, 005 (2021) · published 24 February 2021 | · pdf

We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensor-network ansatz. We discuss how more reliable results could be obtained.
QMetrology from QCosmology: Study with entangled two qubit open quantum system in De Sitter space

Sayantan Choudhury, Satyaki Chowdhury, Nitin Gupta, Abinash Swain

SciPost Phys. Core 4, 006 (2021) · published 29 March 2021 | · pdf

In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. Quantum Metrology, compared to classical parameter estimation theory, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper we present a new avenue in terms of Quantum Metrology, which beats the classical parameter estimation. We also present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.