Qubit regularized O ( N ) nonlinear sigma models
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Goldstone bosons on celestial sphere and conformal soft theorems
In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in “UV completed theories” (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
U(1) fields from qubits: An approach via D-theory algebra
A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1 + 0 -dimensional ( 1 + 0 -D) matrix models, 1 + 1 -D sigma models and non-Abelian gauge theories in 2 + 1 and 3 + 1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU ( 3 ) field for lattice QCD and other non-Abelian 1 + 1 -D sigma models or 3 + 1 -D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1 + 1 -D sine-Gordon equation. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
Continuous-variable quantum computation of the O(3) model in 1+1 dimensions
We formulate the $O(3)$ non-linear sigma model in $1+1$ dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous variable (CV) approach to quantum computing. Here we construct the ground state and excited states using the coupled cluster ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates, estimate the discretization error, and present numerical results obtained from a photonic quantum simulator. We expect that the methods developed in this work will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decade.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Circles and triangles, the NLSM and Tr(Φ 3 )
A surprising connection has recently been made between the amplitudes for Tr(Φ 3 ) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr(Φ 3 ) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between “circles” and “triangles”, interpreting the equation y = $\sqrt{1 – x^2}$ both as parametrizing points a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr(Φ3) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr(Φ 3 ) theory defines a natural notion of “surface-soft limit” intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken “surface-soft”.
Scattering Amplitudes↗
Double copy for massive scalar field theories
We explore extensions of the double copy to massive theories and find a new cubic theory with a local double copy. We consider the nonlinear sigma model and the special galileon theory, massless versions of which are known to be related through the double copy. We show that by performing a Kaluza-Klein reduction of these theories from five dimensions down to four, a double copy relation exists between the resulting massive four-dimensional scalar field theories. This requires the vanishing contribution of new galileon terms arising in high dimensions. We further explore if other interactions that do not arise from a dimensional reduction of the nonlinear sigma model could be double copied and find a new cubic interaction which satisfies the BCJ relations up to 5-point amplitudes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Thermal partition function of $$ {J}_3{\overline{J}}_3 $$ deformed AdS3
Abstract We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized$$ {J}_3{\overline{J}}_3 $$ J 3 J ¯ 3 deformedAdS 3 with periodic Euclidean time as an integral transform of the partition function of the undeformed EuclideanizedAdS 3 . Such a deformation is interpretable as an irrelevant “single-trace$$ T\overline{T} $$ T T ¯ deformation” of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal$$ J\overline{J} $$ J J ¯ deformation of a sigma model with U(1) L × U(1) R global symmetry. We then describe how this procedure is implemented on SL(2,R) sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed SL(2,R) torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory.
Physics↗
Effective Field Theory of Random Quantum Circuits
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
On small black holes in string theory
Abstract We discuss the worldsheet sigma-model whose target space is thed+1 dimensional Euclidean Schwarzschild black hole. We argue that in the limit where the Hawking temperature of the black hole,T, approaches the Hagedorn temperature,T H , it can be described in terms of a generalized version of the Horowitz-Polchinski effective theory. Ford≥ 6, where the Horowitz-Polchinski EFT [1, 2] does not have suitable solutions, the modified effective Lagrangian allows one to study the black hole CFT in an expansion in powers ofd− 6 andT H −T. AtT=T H , the sigma model is non-trivial for alld> 6. It exhibits an enhanced SU(2) symmetry, and is described by a non-abelian Thirring model with a radially dependent coupling. The resulting picture connects naturally to the results of [3–5], that relate Schwarzschild black holes in flat spacetime at largedto the two dimensional black hole. We also discuss an analogous open string system, in which the black hole is replaced by a system of two separated D-branes connected by a throat. In this system, the asymptotic separation of the branes plays the role of the inverse temperature. At the critical separation, the system is described by a Kondo-type model, which again exhibits an enhanced SU(2) symmetry. At larged, the brane system gives rise to the hairpin brane [6].
Physics↗
Classical integrability of root-$T\overline{T}$ flows
The root-$T\overline{T}$ flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) $T\overline{T}$ flow, and it can be integrated explicitly for a large class of actions, leading to nonanalytic Lagrangians reminiscent of the four-dimensional modified-Maxwell theory (ModMax). It is not a priori obvious whether the root-$T\overline{T}$ flow preserves integrability, as is the case for the $T\overline{T}$ flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the nonlinear sigma models on symmetric and semisymmetric spaces, without or with the Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both root-$T\overline{T}$ and $T\overline{T}$ for all of these models.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Trivializing Flow in 2D-O(3) model
The two dimensional O(3) sigma model, just as quantum chromodynamics, is an asymptotically free theory with a mass gap. Therefore, it is an interesting and simple toy model to investigate algorithms for Markov Chain Monte Carlo simulations of quantum chromodynamics. In this talk, we discuss the construction of a trivializing map, a field transformation from a given theory to a trivial one, through a suitably chosen gradient flow. An analytic solution for the generating functional of this trivializing flow has been obtained by a perturbative expansion in the flow time. Utilizing this solution allows for new approaches to be considered when proposing updates for a Markov Chain Monte Carlo algorithm.
Chamness, Christopher↗
Skyrmions and hopfions in three-dimensional frustrated magnets
Here, a model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic skyrmions. In the continuum approximation, this model reduces to a nonlinear sigma model on a squashed sphere that has a natural interpolating parameter. At one limit of the parameter, the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to hopfions, and in the other limit, it becomes very similar to the 3D Skyrme model. To better understand the relation between hopfions and 3D skyrmions, a model interpolating between the Faddeev-Niemi and the Skyrme models is reconsidered and it is shown that energies of the solitons obey a linear Bogomol'nyi-Prasad-Sommerfeld bound. The 3D skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Three dimensional flow field inside compressor rotor, including blade boundary layers
The space marching code was modified in order to be able to predict the flow field inside a rotor passage, including the blade and hub wall boundary layers. The basic changes incorporated are modifications of the equations so that the code can handle three dimensional configurations with changes in the radial direction (for example changes in stagger angle, blade camber and thickness), extensions and modifications in order to implement a physically realistic turbulence model such as a k sigma model and an algebraic Reynolds stress model.
Pouagare, M.↗
On the black hole/string transition
We discuss aspects of the possible transition between small black holes and highly excited fundamental strings. We focus on the connection between black holes and the self gravitating string solution of Horowitz and Polchinski. This solution is interesting because it has non-zero entropy at the classical level and it is natural to suspect that it might be continuously connected to the black hole. Surprisingly, we find a different behavior for heterotic and type II cases. For the type II case we find an obstruction to the idea that the two are connected as classical solutions of string theory, while no such obstruction exists for the heterotic case. We further provide a linear sigma model analysis that suggests a continuous connection for the heterotic case. We also describe a solution generating transformation that produces a charged version of the self gravitating string. This provides a fuzzball-like construction of near extremal configurations carrying fundamental string momentum and winding charges. We provide formulas which are exact in α' relating the thermodynamic properties of the charged and the uncharged solutions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Winding θ and destructive interference of instantons
While the θ dependence of field theories is 2π periodic, the ground-state wavefunctions at θ and θ + 2π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d CP N-1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the CP N-1 quantum mechanics with the Berry phase.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗