Conveners
Theoretical developments: TR4
- Richard Brower (Boston University)
Theoretical developments: TR4
- Srimoyee Sen (Iowa State University)
Theoretical developments: TR4
- Simon Catterall (Syracuse University)
Theoretical developments: TR4
- Hidenori Fukaya (Osaka Univ.)
Theoretical developments: TR4
- Evan Berkowitz (Forschungszentrum Jรผlich)
Theoretical developments: TR4
- Stephan Durr (University of Wuppertal)
Theoretical developments: TR4
- Aleksey Cherman (University of Minnesota)
Theoretical developments: TR4
- David Tong (Cambridge)
Theoretical developments: TR4
- George Fleming (Fermi National Accelerator Laboratory)
We extend an established strategy to non-perturbatively determine mass-improvement coefficients for heavy valence Wilson fermions in $N_f=3$ massless QCD to effectively cancel higher-order mass-dependent cutoff effects. Using Schrรถdinger functional simulations in physical volumes of $L\simeq0.25,0.5\,$fm we test our strategy by simulating relativistic b-quarks at lattice spacings of $0.008\le...
The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In [1] we have shown how to overcome this limitation for classical actions describing point particle motion, using the world-line formalism of general relativity. The key is to treat coordinate maps (from an abstract parameter space into...
The quantum effective potential is an object, often central in the discussion of spontaneous symmetry breaking, however, it is not directly accessible in lattice simulations. Therefore here we concentrate on the closely related constraint potential. It is defined by a path integral, where all local fluctuations are taken into account but the volume averaged order parameter is fixed. This...
We present results using a novel method for constraining fermionic condensates in a fermionic path integral. This approach enables us to obtain the quantum effective potential in the infinite volume limit, which is typically inaccessible using the standard technique of taking the double limit of infinite volume and zero explicit symmetry breaking. By constraining the relevant order parameter...
The present work is about a new method to sample the quantum fluctuations of relativistic fields by means of a pseudo-Hamiltonian dynamics in an enlarge space of variables. The proposed approach promotes the fictitious time of Parisi-Wu stochastic quantisation to a true physical parameter controlling a deterministic dynamics. The sampling of quantum fluctuations is guaranteed by the presence...
The phenomenon of unpaired Weyl fermions appearing on the sole 2n dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed. Similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We...
Accurate calculations of the nucleation rate $\Gamma$ for first order phase transitions are important for determining their observable consequences in particle physics and cosmology. Perturbative calculations are often used, but they are incomplete and should be tested against fully nonperturbative lattice simulations. We simulate nucleation on the lattice in a scalar field theory with a...
I'll explain how to construct symmetry-preserving lattice regularizations of 2d QED, as well as the `3450' chiral gauge theory. The basic idea is to leverage bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing. We...
The BKT transition in low-dimensional systems with a U(1) global symmetry separates a trivially gapped, disordered phase, and is driven by vortex proliferation. Recent developments in modified Villain actions provide a class of lattice models which have an extra $\mathbb{Z}_W$ global symmetry that counts vortices mod W, mixed 't Hooft anomalies, and persistent order even at finite lattice...
We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge $Q$ operators defined at the lower boundary of the Quantum Chromodynamics conformal window:
\begin{equation}
\tilde{\Delta}Q = \tilde{\Delta}_Q^\ast +\left(\frac{m{\sigma}}{4 \pi \nu}\right)^2 \, Q^{\frac{\Delta}{3}} B_1 + ...
A lattice formulation of non-Abelian chiral gauge theories has long been an open problem. One of the most important developments motivated by this question is the Ginsparg-Wilson (GW) relation, which encodes how the anomalous chiral symmetry "optimally" manifests on the lattice. Developments in condensed-matter physics have uncovered a deep connection between anomalies and topological...
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $\eta$ invariant of the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using the $K$-theory does not require the Ginsparg-Wilson relation or the modified chiral symmetry on the lattice. We prove that...
We formulated axion QED on a lattice using a modified Villain formalism. While the axion-photon coupling in the continuum theory is straightforward, we found that the corresponding coupling in the lattice gauge theory using the modified Villain formalism is more complex. As a result, we discovered that the gauge-invariant 't Hooft loop requires a surface inside it. Additionally, we discussed...
We report our study of the discrete symmetry for lattice 3450 model
proposed by Wang and Wen. .
Lattice 3450 model is expected to describe the anomaly free chiral U(1) gauge theory in 1+1 dimension using 2+1 dimensional domain-wall fermion with gapping interactions for the mirror sector.
We find that the lattice model has exact discrete symmetry in addition to U(1) x U(1)...
The gradient flow method has become an important tool which enables us to efficiently extract the nonperturbative low energy physics from lattice simulations. In this study we perturbatively compute the gradient flow scheme coupling for the SU($N$) twisted EguchiโKawai (TEK) model using the numerical stochastic perturbation theory (NSPT) in the large-$N$ limit. We evaluate the perturbative...
We explore the smoothing properties induced by Wilson flow and their implications on the topological charge. Our study examines the smoothness of the flowed energy density and the topological charge within the framework of orientifold theories. We find that jumps in these quantities can appear even at very large flow times. These jumps in smoothness coincide with changes in the topological...
The energy-momentum tensor in the 2D Ising CFT is constructed on the lattice in both spin and fermionic variables. The expression is confirmed by conformal Ward identities on the torus. We work in hexagonal lattice (and by taking the dual, triangular lattice), which enables us to study it in the full range of the modular parameter $\tau$ [1] and further its role of deforming $\tau$. In...
Lattice radial quantization on cylinders ($\mathbb R \times \mathbb S^{d-1} $), potentially offers a powerful new approach for strong coupling conformal or near conformal field theories, including gauge theories under considerations for Beyond the Standard Model (BSM) composite Higgs and Dark Matter physics. A general solution for any triangulated (or simplicial) lattice manifold was...
We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson-Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis...
We study the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. At zero density we investigate the von Neumann and R\'enyi types of entanglement entropies. The central charge is determined from the asymptotic scaling properties of the entropies. We examine the consistency between two entropies. In the finite density region, where this model suffers...
We use the Grassmann tensor renormalization group method to calculate the free energy of the $N_f=2$ Schwinger model with a $2\pi$ periodic $\theta$ term in a broad range of mass. We confirm the numerical results agree with the analytical ones in the large mass limit, and check the qualitative consistency in the small mass limit. We also calculate the vacuum degeneracy, which is consistent in...
We analyze the phase structure of 2d CP(1) model with $\theta$ term by using the tensor renormalization group method. We propose a new tensor network representation for the model using the quadrature scheme and confirm that its accuracy is improved compared to the previous one. For the coarse-graining algorithm, we employ not only the conventional one but also the bond-weighted one in order to...
The applicability of Symanzik Effective theory (SymEFT) for the description of lattice artifacts assumes a local formulation of the lattice theory. We discuss the symmetries realised by tastes local in spacetime of unrooted staggered quarks, approaching mass-degenerate 4-flavour QCD in the continuum limit. An outlook on some implications for the asymptotic lattice-spacing dependence is given...
We present analytical and numerical results on locality and symmetry properties of staggered fermions with taste splitting mass terms. As staggered species split differently for different types of taste splitting masses, various lattice symmetry subgroups and symmetry properties emerge. Preliminary numerical results are given for lattice sizes up to $8^4$.
Lattice chiral perturbation theory is constructed for the
Karsten-Wilczek (KW) minimally doubled fermion action. Symanzik
expansion based on the symmetries of the lattice KW action and
subsequent spurion analysis have been carried out. This led to
the chiral Lagrangian which can be arranged in powers of quark
masses and lattice spacing.
We determined the eigenspectra of minimally doubled fermions (MDF), in both Karsten-Wilczek and Borici-Creutz realizations, and studied the chiralities of the eigenmodes and topological charges for background SU(3) gauge fields in four spacetime dimensions. We employed the spectral flow of the eigenvalues for this work.
The recent advancements towards scalable fault-tolerant quantum computing have brought excitement about simulating lattice gauge theories on quantum computers. However, digital quantum computers require truncating the infinite-dimensional link Hilbert space to finite dimensions. In this talk, we focus on the $\mathrm{SU}(N)$ gauge theory coupled to $N_f$ flavor of quarks and propose a...
Hadronic scattering amplitudes can be approximated as linear combinations of spatially-smeared Euclidean correlators, sampled at discrete non-coinciding times. The resulting approximation formula holds in infinite-volume continuum QCD, however the approximant has an obvious representation in the discrete finite-volume theory. This observation can be used to design a numerical strategy to...
In recent years, the low-energy physics of gauge theories has been explored through the concept of generalized symmetries, which extends the notion of the traditional symmetry. In this talk, by using a lattice QCD code set, LatticeQCD.jl, we carry out numerical simulations of lattice $SU(N)$ gauge theory coupled with $\mathbb{Z}_N$ $2$-form gauge fields. Such couplings provide a completely...
We study a U(1)-gauged 2-flavor spin system in 3 dimensions. For the gauge fields we use the Villain formulation with a constraint that removes lattice monopoles and in this form couple the gauge fields to 2-component spins. We discuss the simulation strategies for this highly constraint system and present first results for the phase structure.
Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose a yet another...
In the standard lattice domain-wall fermion formulation, two flat domain-walls are put where both of the left- and right-handed massless modes appear on the walls. In this work we investigate a single spherical domain-wall fermion mass term embedded into a flat square three-dimensional lattice. In the free fermion case, we find that a single Weyl fermion appears at the wall and it feels...
We discuss a single domain-wall system with a nontrivial curved background by considering a massive fermion on a 3D square lattice, where the domain-wall is a 2D sphere. In the presence of a topologically nontrivial U(1) link gauge field, we observe the emergence of a zero mode with opposite chirality localized at the center where the gauge field is singular. This results in the low-energy...
The construction of gauge invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but the explicit realization of them is complicated by the difficulties of SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no...
Thermodynamic studies of gauge theories in the presence of a finite fermionic density and in real-time, out-of-equilibrium processes, can be facilitated by Hamiltonian-simulation methods, such as tensor networks and quantum computing. A suitable framework for such studies is quantum thermodynamics, a subfield of thermodynamics that extends traditional thermodynamics to quantum systems. Due to...
Tensor renormalization group is expected to be a promising method to simulate lattice field theories at finite density since it does not suffer from the sign problem. We construct a Grassmann tensor network representing the partition function of 1+1D SU(2) lattice gauge theory coupled with staggered fermions. At finite couplings, a random sampling is applied to discretize the group...
We present a general method to analyze the size dependence of entanglement entropy (EE) within the tensor renormalization group (TRG). Much attention has been paid to the TRG method since it does not suffer from the sign problem and enables us to take the large-volume limit easily. We represent the density matrix of a 1D quantum system as a 2D tensor network and develop a method to calculate...
We use the tensor renormalization group to investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a $\theta$ term. The U(1) gauge action is constructed with Lรผscher's admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find a...
We present a spectroscopy scheme for lattice field theory by using tensor renormalization group method combining with transfer matrix formalism. By using this scheme, we can not only compute the energy spectrum for the lattice theory but also determine the quantum number of the energy eigenstate. Unlike spectroscopy by Monte Carlo algorithm, this scheme can extract the energy spectrum with...
Tensor-network methods are valuable Hamiltonian-simulation methods which enable probing dynamics of strongly-interacting quantum-many-body systems, including gauge theories, without encountering sign problems. They also have the potential to inform efficient quantum-simulation algorithms of the same theories. We develop and benchmark a matrix-product-state (MPS) ansatz for the SU(2) lattice...
As a first step towards semiclassically simulating a gravitationally collapsing spherical symmetric configuration of a scalar quantum field, we numerically study such a system in the quenched case. In this approximation, only the uniquely defined classical part of the stress energy tensor is considered as a source in the Einstein equation. While avoiding complications with renormalization,...
We argue the feasibility to study the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a novel method and successfully test it in application to the Schwinger model in the presence of a topological $\theta$-term. We explore the first-order-phase-transition and the no-transition regions of the corresponding phase diagram. The core...
