Conveners
Theoretical Developments
- Evan Berkowitz (Forschungszentrum Jülich)
Theoretical Developments
- Simon Catterall (Syracuse University)
Theoretical Developments
- Yigal Shamir (Tel Aviv University)
Theoretical Developments
- Shinichiro Akiyama (The University of Tokyo)
Theoretical Developments
- Okuto Morikawa (Osaka University)
Theoretical Developments
- Xiaoyong Jin (ANL)
Hamiltonian truncation is a quantum variational method that approximates the ground state by minimizing the energy on a finite truncated basis of Hilbert space. A straightforward application of this method to quantum field theory would seem to be hopeless, since generic states in the Hilbert space have an exponentially small overlap with physical states. Nonetheless, this talk will present...
Qubit regularization provides a framework for studying gauge theories through finite-dimensional local Hilbert spaces, presenting opportunities for digital quantum simulations. In this talk, we investigate the IR phases of 2d QCD with the $\mathrm{SU}(N)$ gauge group via qubit regularization. In the continuum, a 2d $\mathrm{SU}(N)$ gauge theory coupled to a single flavor of fundamental...
Other than the commonly used Wilson’s regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming era of quantum simulations of QFTs. A notable example is Euclidean qubit regularization, which provides a natural way to recover continuum QFTs that emerge...
We consider gauge theories on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green-Schwarz mechanism, between the $1$-form center and $\mathbb{Z}_p$ $3$-form symmetries. Following recent studies of the lattice construction of the...
We extend the definition of L\"uscher's lattice topological charge to the case
of $4$d $SU(N)$ gauge fields coupled with $\mathbb{Z}_N$ $2$-form gauge fields.
This result is achieved while maintaining the locality, the $SU(N)$ gauge
invariance, and $\mathbb{Z}_N$ $1$-form gauge invariance, and we find that the
manifest $1$-form gauge invariance plays the central role in our...
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a well-defined continuum limit. I perform Monte Carlo simulations of the critical Ising model on discretizations of a 2-sphere and I show that the simulations are in...
A general geometrical framework is explored for quantum field theory on curved manifolds motivated by the recent map of the 2d Ising model on a triangulated grid to reproduce the integrable conformal field theory (CFT) on the modular torus ($\mathbb T^2$) and the Riemann sphere ($\mathbb S^2$). This talk will emphasize the special role of affine transformations as a bridge between...
At its critical point, the three-dimensional Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. While the critical exponents of the Ising model, which are related to the scaling dimensions of certain primary operators of the CFT, have been well-investigated in lattice calculations over the past few decades, the theory’s operator product expansion (OPE) coefficients...
Dynamical Triangulations might provide a tool to discover asymptotic safety in quantum gravity. This scenario is based on scale invariance which is realized at an interacting fixed point of the renormalization group flow. In this spirit, asymptotically safe quantum gravity is a quantum field theoretic approach to quantum gravity. On the lattice, asymptotic safety would be realized as a...
I will discuss a discretization of Euclidean, weak-field General Relativity allowing the generation of a Markov chain of dynamic, pure gravity spacetimes at non-zero temperature via Metropolis algorithm with importance sampling. A positive action conjecture is implemented on the lattice, ensuring a probabilistic interpretation of exp(-S) and that dS=0 yields the Einstein field equations....
The conventional discretisation of space-time entails a breaking of continuum symmetries and spoils the conservation of the associated Noether charges with ramifications for particle spectra and the renormalisation of central quantities, such as the Energy Momentum Tensor on the lattice.
In this work [1] we take first steps towards discretizing classical actions, while retaining its continuum...
We report on a lattice fermion formulation with
a curved domain-wall mass term to nonperturbatively
describe fermions in a gravitational background.
In our previous work in 2022, we showed in the free
fermion theory on one and two-dimensional spherical domain-walls
that the spin connection is induced on the lattice
in a consistent way with continuum theory.
In this talk we add...
Minimally doubled fermions realize one degenerate pair of Dirac fermions on the lattice. Similarities to staggered fermions exist, namely, spin and taste degrees of freedom become intertwined, and a remnant, non-singlet chiral symmetry and ultralocality are maintained. However, charge conjugation, isotropy and some space-time reflection symmetries are broken by the cutoff.
For two variants,...
We present a novel approach to construct effective descriptions of a confining string. We consider a string pinned with heavy quark-antiquark endpoints on the lattice Yang-Mills theory (Kogut-Susskind Hamiltonian) as background with $SU(N_c)$ gauge symmetry with large $N_c$. Our approach describes the dynamics of the confining string as two different spin chains, which are both integrable. In...
Laboratory setups and astrophysical circumstances may confine fermions to two spatial dimensions. Leading-order nonrelativistic pionless EFT in 2D has an anomalously broken conformal symmetry, and exhibits BKT phase transition. We use classic tools from lattice field theory to make predictions about this strongly correlated system.
Gapped fermion theories with gapless boundary fermions can exist in any number of dimensions.
When the boundary has even space-time dimensions and hosts chiral fermions, a quantum Hall current
flows from the bulk to the boundary in a background electric field. This current compensate for the
boundary chiral anomaly. Such a current inflow picture is absent when the boundary theory is...
We present a method for analytic continuation of Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic in the upper half plane. A novel aspect of our method is rigorous bounding of systematic uncertainties, which are handled by constructing the full space of interpolating functions (at each...
The minimal renormalon subtraction introduced by Komijani and used by the Fermilab Lattice, MILC, and TUMQCD Collaborations to determine quark masses is extend to other quantities. A simpler derivation of the renormalon normalization is presented, showing at the same time how it is completely general. The scale dependence of the Borel sum is investigated.
Beyond spectral quantities, Symanzik Effective Theory (SymEFT) predictions of the asymptotic lattice-spacing dependence require the inclusion of an additional minimal basis of higher-dimensional operators for each local field involved in the matrix element of interest. Adding the proper bases for fermion bilinears of mass-dimension 3 allows to generalise previous predictions to matrix elements...
Stochastic locality, arising from the mass gap of QCD, allows for independent fluctuations in distant regions of lattice gauge field configurations.
This can be used to increase statistics and, in the extreme case of the master-field approach, obtain an error estimate from a single configuration.
However, spatially-separated samples at moderate distances show residual correlation that needs...
We present a proposal for calculating the running of the coupling constant of the $SU(3)$ pure gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions (PTBC). The TGF is a gradient flow-based renormalization scheme formulated in an asymmetric lattice with twisted boundary conditions. Combined with step scaling, it has...
Triviality of phi4 theory in four dimensions can be avoided if the bare coupling constant is negative in the UV. Theories with negative coupling can be put on the lattice if the integration domain for phi(x) is contour-deformed from the real to the complex domain. In 0+1d (quantum mechanics), one can recover results from PT-symmetric quantum mechanics in this way. In this talk, I report on an...
Novel regularizations of lattice gauge theories can potentially enable faster classical or quantum simulation, but the landscape of available regularizations and their continuum limits is not fully understood. Our recent work adds a point to this landscape by introducing a generalization of U(1) lattice gauge theory obtained by applying a boundary condition in group space with a twist angle...
We study the three dimensional principal chiral model using both the triad tensor renormalization group method, and the anisotropic tensor renormalization group method. We present a tensor network formulation for the model, and compare the ability of the two methods to measure thermodynamic observables. In addition we remark upon criticality, and the possible universality class of the phase...
Bond-weighted tensor renormalization group (BTRG) is a novel tensor network algorithm to improve the accuracy in calculating the partition functions of the classical spin models. We extend the BTRG to make it applicable for the fermionic system, benchmarking with the two-dimensional massless Wilson fermion. We show that the accuracy with the fixed bond dimension is improved also in the...
We present a study of the 3D O(2) non-linear $\sigma$-model on the lattice, which manifests topological defects in the form of vortices. They tend to organize into vortex lines that bear strong analogies with global cosmic strings. Therefore, this model serves as a testbed for studying topological defects. Moreover, the model undergoes a second-order phase transition, hence it is appropriate...
We simulate lattice QED in (strong) external electromagnetic fields using techniques developed for simulating lattice QCD. We are currently simulating lattice QED in constant external magnetic fields to observe the chiral symmetry breaking predicted by Schwinger-Dyson studies. Difficulties in extending these studies to include external electric fields are discussed.
The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon, as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in continuum and numerically on a lattice, by adding the Wilson term and smearing...
In this talk, we present the equivalence between the Wilson flow and the stout smearing. The similarity between these two methods was first pointed out by Lüscher’s original paper on the Wilson flow. We first show the analytical equivalence of two methods, which indicates that the finite stout smearing parameter induces $O(a^2)$ correction. We secondly show that they remain equivalent in...
Two popular methods to reduce discretisation effects are Symanzik improvement and gauge field smearing in the Dirac operator. Tree-level $O(a^2)$-improved Wilson fermions can be obtained from $O(a)$-improved Wilson fermions by adding one dimension-6 operator to the action. For gauge field smearing one wants to avoid the situation when too much smearing leads to uncontrolled continuum...
The pion decay constant $F_\pi$ plays an important role in QCD
and in Chiral Perturbation Theory. It is hardly known, however,
that a corresponding constant exists in the Schwinger model with
$N_f \geq 2$ degenerate fermion flavors. In this case, the "pion"
does not decay and $F_\pi$ is dimensionless. Still, $F_\pi$ can be
defined by 2d analogies to the Gell-Mann--Oakes--Renner...
The $O(N)$-Nonlinear Sigma Model (NLSM) is an example of field theory on a target space with non-trivial geometry. One interesting feature of NLSM is asymptotic freedom, which makes perturbative calculations interesting.
Given the successes in Lattice Gauge Theories, Numerical Stochastic Perturbation Theory (NSPT) is a natural candidate for performing high order computations also in the case...
We study a 3-dimensional SU(2) gauge theory with 4 Higgs fields which
transform under the adjoint representation of the gauge group,
that has been recently proposed by Sachdev et al. to explain the physics
of cuprate superconductors near optimal doping. The symmetric
confining phase of the theory corresponds to the usual
Fermi-liquid phase while the broken (Higgs) phase is associated...