How Bosonic Fields behave(Field Theory + Physics)
1. Bosonic field digitization for quantum computers(arXiv)
Author : Alexandru Macridin, Andy C. Y. Li, Stephen Mrenna, Panagiotis Spentzouris
Abstract : Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods to accurately predict error scaling as a function of the resolution and parameters of the model that can be implemented efficiently on quantum hardware. In this paper, we address the representation of lattice bosonic fields in a discretized field amplitude basis, develop methods to predict error scaling, and present efficient qubit implementation strategies. A low-energy subspace of the bosonic Hilbert space, defined by a boson occupation cutoff, can be represented with exponentially good accuracy by a low-energy subspace of a finite size Hilbert space. The finite representation construction and the associated errors are directly related to the accuracy of the Nyquist-Shannon sampling and the Finite Fourier transforms of the boson number states in the field and the conjugate-field bases. We analyze the relation between the boson mass, the discretization parameters used for wavefunction sampling and the finite representation size. Numerical simulations of small size Φ4 problems demonstrate that the boson mass optimizing the sampling of the ground state wavefunction is a good approximation to the optimal boson mass yielding the minimum low-energy subspace size. However, we find that accurate sampling of general wavefunctions does not necessarily result in accurate representation. We develop methods for validating and adjusting the discretization parameters to achieve more accurate simulations
2. Universal Mass Scale for Bosonic Fields in Multi-Brane Worlds(arXiv)
Author : R. I. de Oliveira Junior, G. Alencar, R. R. Landim, R. N. Costa Filho
Abstract : In this paper we find an universal mass scale for all p−forms in multi-brane worlds model. It is a known fact the this model provides an ultralight mode for the fields. However, to get this, the Lagrangians considered in the literature are not covariant. In order to solve this, we propose a covariant version to multi-localize q−form fields. As a consequence of the covariance, we show that all the q-form fields have an ultralight mode with the same mass that the gravitational one. That way we show that there is an universal mass scale for the ultralight modes of the bosonic fields. This suggests that a new physics must emerge, for all theses fields, at the same scale. After that, we revisit the results that consider a crystal manyfold background in the Randall-Sundrum scenary (RS), and add the discussion related to geometrical couplings in such a configuration. The wave functions of fields trapped in the crystal are Bloch-like waves, and their behavior is very similar to electrons inside a lattice, just like in the Kronig-Penney model (KP). We compute the mass dispersion relations for those fields with and without a dilaton coupling. It leads to new results for the band gap structure of these fields. In the case of the Kalb-Ramond field, and with the correct dispersion relation, there is no gap between the mass bands. Also, always that the field is coupled with the dilaton, its first mass mode decreases. When the generalization to the q−form is done, we show that it is not possible to suppress or generate mass for the fields by controlling the dilaton coupling, differently of what was argued previously.
3.Qubitization strategies for bosonic field theories (arXiv)
Author : Andrei Alexandru, Paulo F. Bedaque, Andrea Carosso, Michael J. Cervia, Andy Sheng
Abstract : Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two different truncations that preserve the symmetries of the 1+1-dimensional O(3) non-linear σ-model — one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative geometry. We compare the spectrum of the truncated theories in a finite box with the full theory. We use open boundary conditions, a novel method that improves on the correlation lengths accessible in our calculations. We provide evidence that the angular-momentum truncation fails to reproduce the σ-model and that the anti-ferromagnetic fuzzy model agrees with the full theory
4. Pole-skipping in holographic theories with bosonic fields(arXiv)
Author : Diandian Wang, Zi-Yue Wang
Abstract : We study the phenomenon of pole-skipping in holographic CFTs dual to diffeomorphism invariant theories containing an arbitrary number of bosonic fields in the large N limit. Defining a weight to organize the bulk equations of motion and field components, a set of general pole-skipping conditions are derived. In particular, the frequencies simply follow from general covariance and weight matching. Relating the highest-weight pole-skipping frequency to an exponential growth rate, i.e., the Lyapunov exponent, we show that the chaos bound is generally violated in the presence of finitely many higher spin fields, consistent with existing evidence. In the absence of such pathological fields, we show that the energy density Green’s function has its highest-weight pole-skipping happening at a location related to the OTOC for arbitrary higher-derivative gravity, with a Lyapunov exponent saturating the chaos bound and a butterfly velocity matching that extracted from a shockwave calculation. We also suggest a physical explanation for this matching by obtaining the shockwave metric from a regularized limit of the metric perturbation at the skipped pole.
