Bosonic Quantum Field Theories Research Articles

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

A post-Gaussian approach to dipole symmetries and interacting fractons

We use a post-Gaussian variational approach to non-perturbatively study a general class of interacting bosonic quantum field theories with generalized dipole symmetries and fractonic behavior. We find that while a Gaussian approach allows to carry out a consistent renormalization group (RG) flow analysis of these theories, this only grasps the interaction terms associated with the longitudinal motion of dipoles, which is consistent with previous analysis using large N techniques. Remarkably, our post-Gaussian proposal, by providing a variational improved effective potential, can capture the transverse part of the interaction between dipoles in such a way that a non-trivial RG flow for this term is obtained and analyzed. Our results suggest that dipole symmetries that manifest due to the strong coupling of dipoles, may robustly emerge at low energies from short-distance models without that symmetry.

Spin-half bosons with mass dimension three-half: Evading the spin-statistics theorem

By exploiting the freedom in defining the dual of spinors, we report an unexpected theoretical discovery of a quantum field theory of spin-half bosons. It fulfils Dirac's 1969-70 observation that “there must be boson variables connected with electrons”. The theory is local, Lorentz invariant, and has a positive-definite Hamiltonian. We formulate the unitarity-preserving scattering theory to accommodate the new dual and the associated adjoint. A model of Yukawa interaction with spin-half bosons and fermions of equal masses is studied to explicitly show unitarity.

Nearly Optimal Quantum Algorithm for Generating the Ground State of a Free Quantum Field Theory

Generating the ground state of a free massive scalar bosonic quantum field theory: two quantum algorithms with nearly optimal runtimes are devised, delivering super-quadratic speedup over the state-of-the-art.

Universality of a truncated sigma-model

Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a “qubitization”), so only the space continuum limit is required. A qubitization of the 1+1 dimensional asymptotically free O(3) nonlinear σ-model based on ideas of non-commutative geometry was previously proposed [1] and, in this paper, we provide evidence that it reproduces the physics of the σ-model both in the infrared and the ultraviolet regimes.

Linear bosonic quantum field theories arising from causal variational principles

It is shown that the linearized fields of causal variational principles give rise to linear bosonic quantum field theories. The properties of these field theories are studied and compared with the axioms of local quantum physics. Distinguished quasi-free states are constructed.

Tree level integrability in 2d quantum field theories and affine Toda models

We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle production and diagonal scattering, at tree level. For theories satisfying what we call ‘simply-laced scattering conditions’, by which we mean that poles in inelastic 2 to 2 processes cancel in pairs, and poles in allowed processes are only due to one on-shell propagating particle at a time, the requirement that all inelastic amplitudes must vanish is shown to imply the so-called area rule, connecting the 3-point couplings {C}_{abc}^{(3)} to the masses ma, mb, mc of the coupled particles in a universal way. We prove that the constraints we find are universally satisfied by all affine Toda theories, connecting pole cancellations in amplitudes to properties of the underlying root systems, and develop a number of tools that we expect will be relevant for the study of loop amplitudes.

Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes

According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2G̃aF−G̃F+G̃A−G̃R in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2G̃aF−G̃F, which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.

L\xfcscher-corrections for 1-particle form-factors in non-diagonally scattering integrable quantum field theories

In this paper we derive from field theory a Lüscher-formula, which gives the leading exponentially small in volume corrections to the 1-particle form-factors in non-diagonally scattering integrable quantum field theories. Our final formula is expressed in terms of appropriate expressions of 1- and 3-particle form-factors, and can be considered as the generalization of previous results obtained for diagonally scattering bosonic integrable quantum field theories. Since our formulas are also valid for fermions and operators with non-zero Lorentz-spin, we demonstrated our results in the Massive Thirring Model, and checked our formula against 1-loop perturbation theory finding perfect agreement.

Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automata for distinguishable particles based on two different quantum walks, and show that by restricting to the antisymmetric and symmetric subspaces, respectively, a multiparticle theory for free fermions and bosons in three spatial dimensions can be produced. This construction evades a no-go theorem that prohibits the usual fermionization constructions in more than one spatial dimension. In the long-wavelength limit, these recover Dirac field theory and Maxwell field theory, i.e., free QED.

QFT and Topology in Two Dimensions: $$\mathrm{SL}(2, {{\mathbb {R}}})$$-Symmetry and the de Sitter Universe

We study bosonic quantum field theory on the double covering \(\widetilde{dS}_{2}\) of the two-dimensional de Sitter universe, identified to a coset space of the group \(\mathrm{SL}(2, {{\mathbb {R}}})\). The latter acts effectively on \(\widetilde{dS}_{2}\) and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime \({dS}_2\); it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes, however, drastic differences between the two models. We classify all the \(\mathrm{SL}(2, {{\mathbb {R}}})\)-invariant two-point functions and show that: (1) there is no Hawking–Gibbons temperature; (2) there is no covariant field theory solving the Klein–Gordon equation with mass less than 1/2R , i.e., the complementary fields go away.

Gaussian continuous tensor network states for simple bosonic field theories

Tensor networks states allow one to find the low-energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow one to renormalize away simple divergences variationally. In the end our study makes it plausible that CTNSs are indeed a good manifold to approximate the low-energy states of QFTs.Received 18 December 2020Accepted 9 March 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023059Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum field theory (low energy)TechniquesTensor network methodsVariational approachQuantum Information

Entanglement entropy of excited states in the quantum Lifshitz model

In this work we calculate the entanglement entropy of certain excited states of the quantum Lifshitz model (QLM). The QLM is a 2 + 1-dimensional bosonic quantum field theory with an anisotropic scaling symmetry between space and time that belongs to the universality class of the quantum dimer model and its generalizations. The states we consider are constructed by exciting the eigenmodes of the Laplace–Beltrami operator on the spatial manifold of the model. We perform a replica calculation and find that, whenever a simple assumption is satisfied, the bipartite entanglement entropy of any such excited state can be evaluated analytically. We show that the assumption is satisfied for all excited states on the rectangle and for almost all excited states on the sphere and provide explicit examples in both geometries. We find that the excited state entanglement entropy obeys an area law and is related to the entanglement entropy of the ground state by two universal constants. We observe a logarithmic dependence on the excitation number when all excitations are put onto the same eigenmode.

Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferromagnetic and antiferromagnetic cases. While for the limiting case of the isotropic long-range XY model we can extract the elementary one-quasiparticle dispersion analytically and calculate two-quasiparticle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $\ensuremath{\nu}$ analytically by a bosonic quantum-field theory.

Classical limits of unbounded quantities by strict quantization

This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories with particular attention to number operators and Hamiltonians. The methods take classical limits in a representation-independent manner and so allow one to compare quantities appearing in inequivalent Fock space representations.

Quantum Information Hidden in Quantum Fields

We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a manner that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly of performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT’s internal quantum network. Finally, the entropic equilibrium of fully mixed and maximally entangled states in the quantum network seems to suggest that the black hole paradox of information loss might be solved under suitable conditions.

Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals

Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.

Momentum-space entanglement after smooth quenches

We compute the total amount of entanglement produced between momentum modes at late times after a smooth mass quench in free bosonic and fermionic quantum field theories. The entanglement and Rényi entropies are obtained in closed form as a function of the parameters characterizing the quench protocol. For bosons, we show that the entanglement production is more significant for light modes and for fast quenches. In particular, infinitely slow or adiabatic quenches do not produce any entanglement. Depending on the quench profile, the decrease as a function of the quench rate delta t can be either monotonic or oscillating. In the fermionic case the situation is more subtle and there is a critical value for the quench amplitude above which this behavior is changed and the entropies become peaked at intermediate values of momentum and of the quench rate. We also show that the results agree with the predictions of a Generalized Gibbs Ensemble and obtain explicitly its parameters in terms of the quench data.

On the unsolvability of bosonic quantum fields

ABSTRACTTwo general unsolvability arguments for interacting bosonic quantum field theories are presented, based on Dyson–Schwinger equations on the lattice and cardinality considerations. The first argument is related to the fact that, on a lattice of size N, the system of lattice Dyson–Schwinger equations closes on a basis of ‘primitive correlators’ which is finite, but grows exponentially with N. By properly defining the continuum limit, one finds for a countably infinite basis of the primitive correlators. The second argument is that any conceivable exact analytic calculation of the primitive correlators involves, in the continuum limit, a linear system of coupled partial differential equations on an infinite number of unknown functions, namely the primitive correlators, evolving with respect to an infinite number of independent variables.

Concentration of cylindrical Wigner measures

In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to prove the concentration of all the corresponding cylindrical Wigner measures as Radon measures on suitable topological vector spaces. The analysis is motivated by variational and dynamical problems in the semiclassical study of bosonic quantum field theories.