Field Theory Simulations Research Articles

Magic of discrete Lattice Gauge theories

Simulation of quantum field theories and fundamental interactions is one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for [Formula: see text] LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

Self-consistent field theory for loop-containing polymers: A general algorithm for path-determination

An algorithm was developed for self-consistent field theory (SCFT) simulations of loop-containing polymers (LCPs), where the total number of independent loops (fundamental cycles in the polymer structure) is characterized by the “cycle rank.” Although various multi-ring and cage-like polymers have been reported, there is no explicit SCFT scheme for LCPs with multiple loops. An LCP was cut to open its fundamental cycles to form a pseudo-tree-like polymer. Conventional SCFT calculations for pseudo-tree-like polymers require extra spatial constraints on the pseudo-free endpoints generated by opening the fundamental cycle, which increases the computational cost. A reduction in the computational cost was observed, and the algorithm was applied to microphase-separated structures of small LCPs.

Evolution of current-carrying string networks

Cosmic string networks are expected to form in early Universe phase transitions via the Kibble mechanism and are unavoidable in several Beyond the Standard Model theories. While most predictions of observational signals of string networks assume featureless Abelian-Higgs or Nambu-Goto string networks, in many such extensions the networks can carry additional degrees of freedom, including charges and currents; these are often generically known as superconducting strings. All such degrees of freedom can impact the evolution of the networks and therefore their observational signatures. We report on the results of 20483 field theory simulations of the evolution of a current-carrying network of strings, highlighting the different scaling behaviours of the network in the radiation and matter eras. We also report the first numerical measurements of the coherence length scales for the charge and current and of the condensate equation of state, and show that the latter mainly depends on the expansion rate, with chirality occurring for the matter era. Qualitatively, the fact that the matter era is the optimal expansion rate for these networks to reach scaling is in agreement with recent analytic modelling.

Structures of neural network effective theories

We develop a diagrammatic approach to effective field theories (EFTs) corresponding to deep neural networks at initialization, which dramatically simplifies computations of finite-width corrections to neuron statistics. The structures of EFT calculations make it transparent that a single condition governs criticality of all connected correlators of neuron preactivations. Understanding of such EFTs may facilitate progress in both deep learning and field theory simulations. Published by the American Physical Society 2024

Effective model for superconductivity in magic-angle graphene

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge 2e and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1)×Z2. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation. Published by the American Physical Society 2024

Diffusion models as stochastic quantization in lattice field theory

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.

Curvature perturbations from preheating with scale dependence

We extend the formalism to calculate non-Gaussianity of primordial curvature perturbations produced by preheating in the presence of a light scalar field. The calculation is carried out in the separate universe approximation using the non-perturbative delta N formalism and lattice field theory simulations. Initial conditions for simulations are drawn from a statistical ensemble determined by modes that left the horizon during inflation, with the time-dependence of Hubble rate during inflation taken into account. Our results show that cosmic variance, i.e., the contribution from modes with wavelength longer than the size of the observable universe today, plays a key role in determining the dominant contribution. We illustrate our formalism by applying it to an observationally-viable preheating model motivated by non-minimal coupling to gravity, and study its full parameter dependence.

New basis for Hamiltonian SU(2) simulations

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories. Published by the American Physical Society 2024

Manipulating the processing window of directed self-assembly in contact hole shrinking with binary block copolymer/homopolymer blending

Manipulating the processing window of directed self-assembly in contact hole shrinking with binary block copolymer/homopolymer blending

Lattice real-time simulations with learned optimal kernels

We present a simulation strategy for the real-time dynamics of quantum fields, inspired by reinforcement learning. It builds on the complex Langevin approach, which it amends with system-specific prior information, a necessary prerequisite to overcome this exceptionally severe sign problem. The optimization process underlying our machine-learning approach is made possible by deploying inherently stable solvers of the complex Langevin stochastic process and a novel optimality criterion derived from insight into so-called boundary terms. This conceptual and technical progress allows us to both significantly extend the range of real-time simulations in 1+1d scalar field theory beyond the state of the art and to avoid discretization artifacts that plagued previous real-time field theory simulations. Limitations of and promising future directions are discussed. Published by the American Physical Society 2024

Cage occupancies of CH4, CO2, and Xe hydrates: Mean field theory and grandcanonical Monte Carlo simulations.

We propose a statistical mechanical theory for the thermodynamic stability of clathrate hydrates, considering the influence of the guest-guest interaction on the occupancies of the cages. A mean field approximation is developed to examine the magnitude of the influence. Our new method works remarkably well, which is manifested by two sorts of grandcanonical Monte Carlo (GCMC) simulations. One is full GCMC, and the other is designed in the present study for clathrate hydrates, called lattice-GCMC, in which each guest can be adsorbed at one of the centers of the cage. In the latter simulation, only the guest-guest interaction is explicitly treated, incorporating the host-guest interaction into the free energy of the cage occupation without other guests. Critical phenomena for guest species, such as large density fluctuations, are observed when the temperature is low or the guest-guest interaction is strong.

Real-time dynamics of false vacuum decay

We investigate false vacuum decay of a relativistic scalar field initialized in the metastable minimum of an asymmetric double-well potential. The transition to the true ground state is a well-defined initial-value problem in real time, which can be formulated in nonequilibrium quantum field theory on a closed time path. We employ the nonperturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion. We also compare to classical-statistical field theory simulations on a lattice in the high-temperature regime. By this, we demonstrate that the real-time decay rates are comparable to those obtained from the conventional Euclidean (bounce) approach. In general, we find that the decay rates are time dependent. For a more comprehensive description of the dynamics, we extract a time-dependent effective potential, which becomes convex during the nonequilibrium transition process. By solving the quantum evolution equations for the one- and two-point correlation functions for vacuum initial conditions, we demonstrate that quantum corrections can lead to transitions that are not captured by classical-statistical approximations. Published by the American Physical Society 2024

Quantum computing for nuclear physics

Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for systems ranging from dense non-equilibrium matter, to low-energy nuclear structure and reactions, to high-energy collisions. I present an overview of digital quantum simulations in nuclear physics, with select examples relevant for studies of quark matter.

In silico design of misfolding resistant proteins: the role of structural similarity of a competing conformational ensemble in the optimization of frustration.

Most state-of-the-art in silico design methods fail due to misfolding of designed sequences to a conformation other than the target. Thus, a method to design misfolding resistant proteins will provide a better understanding of the misfolding phenomenon and will also increase the success rate of in silico design methods. In this work, we optimize the conformational ensemble to be selected for negative design purposes based on the similarity of the conformational ensemble to the target. Five ensembles with different degrees of similarity to the target are created and destabilized and the target is stabilized while designing sequences using mean field theory and Monte Carlo simulation methods. The results suggest that the degree of similarity of the non-native conformations to the target plays a prominent role in designing misfolding resistant protein sequences. The design procedures that destabilize the conformational ensemble with moderate similarity to the target have proven to be more promising. Incorporation of either highly similar or highly dissimilar conformations to the target conformation into the non-native ensemble to be destabilized may lead to sequences with a higher misfolding propensity. This will significantly reduce the conformational space to be considered in any protein design procedure. Interestingly, the results suggest that a sequence with higher frustration in the target structure does not necessarily lead to a misfold prone sequence. A successful design method may purposefully choose a frustrated sequence in the target conformation if that sequence is even more frustrated in the competing non-native conformations.

Self-consistent field theory and coarse-grained molecular dynamics simulations of pentablock copolymer melt phase behavior

Using a combined theory-simulation approach we rapidly screen a large polymer design space to identify rules for desired morphologies as well as the chain conformations associated with the theory-predicted phase behavior.

Molecular conformations of dumbbell-shaped polymers in good solvent.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

The Higgs condensate as a quantum liquid: A critical comparison with observations

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper, we compare the triviality scenario and the renormalized two-loop perturbation theory to precise and extensive results from nonperturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalized perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper, we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behaves like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes [Formula: see text], while in the preliminary Run 2 data there are hints of the decays [Formula: see text] in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.

Q-lump scattering

Q-lumps are spinning planar topological solitons with stationary solutions that satisfy first-order Bogomolny equations. Q-lump scattering has previously been studied only in the charge two sector, by approximating time evolution by motion in the moduli space of stationary solutions. In this paper, higher charge scattering is studied via motion on families of 4-dimensional submanifolds of moduli space, obtained by imposing cyclic symmetries. The results are shown to be in good agreement with field theory simulations, which are then applied to study more complicated Q-lump scattering processes, including examples where the moduli space approximation is not applicable. A variety of exotic scattering events are presented.

Fractonic Luttinger liquids and supersolids in a constrained Bose-Hubbard model

Dynamical constraints have drastic consequences for the properties of many-particle quantum systems. Here, the authors study the quantum ground state phases in a fracton system of interacting bosons with dipole conservation. Through a combination of low-energy field theory and tensor network simulations, they identify a novel dipole Luttinger liquid phase as well as a fracton analogue of a supersolid state.

The dynamics of domain wall strings

We study the dynamics of domain wall solitons in (2+1)d field theories. These objects are extended along one of the spatial directions, so they also behave as strings; hence the name of domain wall strings. We show analytically and numerically that the amount of radiation from the propagation of wiggles on these objects is negligible except for regions of high curvature. Therefore, at low curvatures, the domain wall strings behave exactly as the Nambu-Goto action predicts. We show this explicitly with the use of several different numerical experiments of the evolution of these objects in a lattice. We then explore their dynamics in the presence of internal mode excitations. We do this again by performing field theory simulations and identify an effective action that captures the relevant interactions between the different degrees of freedom living on the string. We uncover a new parametric resonance instability that transfers energy from the internal mode to the position of the domain wall. We show that this instability accelerates the radiation of the internal mode energy. We also explore the possibility of exciting the internal mode of the soliton with the collision of wiggles on the domain wall. Our numerical experiments indicate that this does not happen unless the wiggles have already a wavelength of the order of the string thickness. Finally, we comment on the possible relevance of our findings to cosmological networks of defects. We argue that our results cast some doubts on the significance of the internal modes in cosmological applications beyond a brief transient period right after their formation. This, however, should be further investigated using cosmological simulations of our model.