Simulation of finite density lattice QCD at imaginary chemical potential is a popular workaround for the sign problem. One is then left with the problem of performing the analytic continuation of results to the real axis. We show how this continuation can be mapped to an inverse problem via the (integral) Cauchy formula.
Analytic continuation is a central step in the simulation of finite-temperature field theories in which numerically obtained Matsubara data are continued to the real frequency axis for a physical interpretation. Numerical analytic continuation is considered to be an ill-posed problem where uncertainties on the Matsubara axis are amplified exponentially. Here, we present a systematic and...
The QCD cross-over line in the temperature ($T$) -- baryo-chemical potential ($\mu_B$) plane has been computed by several lattice groups by calculating the chiral order parameter and its susceptibility at finite values of $\mu_B$. In this work we focus on the deconfinement aspect of the transition between hadronic and Quark Gluon Plasma (QGP) phases. We define the deconfinement temperature as...
We present recent advancements towards the alleviation of the sign problem for the Hubbard model away of half filling. We couple the thimble decomposition approach with certain approximations, which allow us to predict the structure of the thimble decomposition in advance, before actual Quantum Monte Carlo simulations.
First, we show that the saddle points for the Hubbard model with...
Quantum mechanical theories have an underlying convex geometry defined by the fact that the Hilbert-space norm is positive definite. Positivity is a surprisingly strong constraint, which when combined with other information (such as lattice data, Schwinger-Dyson relations, or equations of motion), allows one to establish qualitatively tight bounds on the behavior of many quantum systems,...
We demonstrate a method to study the phase diagram of a quantum system on quantum devices via adiabatic preparation of states. The method is a direct application of the adiabatic theorem due to M. Born and V. Fock, Z. Phys. 51, 165 (1928). The key idea of the method is to individually evolve the ground state and the first-excited state using a Hamiltonian whose parameters are time-dependent....
The phase diagram of QCD at finite densities remains numerically inaccessible by classical computations. Quantum computers, with their potential for exponential speedup, could overcome this challenge. However, their current physical implementations are affected by quantum noise. In this contribution, I will introduce a novel quantum error mitigation technique based on a BBGKY-like hierarchy,...
Cluster algorithms are Monte Carlo algorithms that provide efficient non-local updates of the configurations. They can avoid critical slowing down when approaching a second-order phase transition and solve severe sign problems in well-tailored cases. The clusters group degrees of freedom that can be updated independently of one another. While highly efficient, the range of models that can be...
The Hamiltonian formulation of lattice gauge theories offers a pathway to new quantum and classical simulation techniques, providing new ways to circumvent different sign problems.In this work, we address different formulations of various Abelian gauge theories within the Hamiltonian framework in 1+1 dimensions. Using Correlated Cluster Algorithms, we exactly solve Gauss’s law for...
The phases and phase transitions of low-dimensional quantum magnets are often described using simple quantum spin models. It is an open question how the properties of these systems are affected by a coupling to the environment, which is always present in any experimental realization. One of the simplest setups for such an open quantum system is the spin-boson model where a single spin is...
A formulation of lattice field theory (LFT) for curved manifolds uses the Regge's triangulated (simplicial) manifold for the Einstein Hilbert action that solves the equation of motion (EOM) for classical GR in the continuum. For the metric field, $g_{\mu \nu}(x)$, this is piece-wise constant finite element method (FEM) which applies equally to the classical field PDEs. But quantizing lattice...
I will review several key features associated with the conventional sign problem and argue that for regular interacting fermionic systems none of them applies if the calculation is done with the help of Feynman diagrams. The diagrammatic approach generically solves the computational complexity problem and can be used for obtaining numerical solutions for interacting fermions. I will illustrate...
The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address this issue: series resummation by conformal mapping, changing the nature of the starting point of the expansion by shifted action tools, and applying the...
Qubit regularization may offer a new approach to Hamiltonian lattice gauge theories. If we insist on working with the Kogut Susskind Hamiltonian, one often encounters sign problems even in the pure gauge theory sector. However, since we are ultimately interested in quantum critical points where the form of the Hamiltonian should not play an important role, we can explore if alternate sign...
The complex Langevin method is an approach to solve the sign problem based on a stochastic evolution of the dynamical degrees of freedom. In principle, it solves the sign problem by trading the complex path integral weight for a real probability distribution in complexified field space. However, due to the complexification, the stochastic evolution sometimes converges to an equilibrium...
Real time evolution in QFT poses a severe sign problem, which may be alleviated via a complex Langevin approach.
However, so far simulation results consistently fail to converge with a large real-time extent. A kernel in a complex Langevin equation is known to influence the appearance of the boundary terms, and thus kernel choice can improve the range of real-time extents with correct...
The complex Langevin (CL) method is a promising tool for addressing the numerical sign problem.- Depending on the specific system, CL may produce unreliable results, which necessitates the use of ad-hoc stabilization methods. Building on the connection between CL and Lefschetz thimbles, we develop weight regularizations to enable correct convergence by deforming thimbles in systems with...
Here I present our recently developed strategy to exploit system specific prior knowledge [1], such as space-time symmetries, as a loophole to the computational challenge posed by NP-hard sign problems. As explicit example, I will showcase how complex Langevin simulations of strongly coupled scalar fields [2] can be amended with relevant prior information using learned kernels. Developments...
The Fermi-Hubbard model suffers from a severe sign problem, both for non-zero chemical potentials and on non-bipartite lattices. Over the years, considerable progress has been made in alleviating the sign problem by deforming the integration contour of the path integral into the complex plane. In this talk, I am going to present a surprisingly simple and yet powerful contour deformation by...
In previous work, with Francis Bursa, we considered the approach of addressing the sign problem using simple contour deformations. As a toy model for examining the approach we used the one-dimensional Bose gas with chemical potential. The contour deformations that were considered are local and they lead to simple forms of the Jacobian that can be simulated fast.
However, the periodic...
In this talk, we review recent advances in applying quantum computing to lattice field theory. Quantum technology offers the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. First proof-of-concept simulations of Abelian and non-Abelian gauge theories in...
In this talk, we present an implementation of multiple fermion flavors in both the Kogut-Susskind and Wilson formulations for quantum simulations of (2+1)-dimensional Quantum Electrodynamics (QED). Our first results show a particular type of level crossing with one flavor of fermions at zero density, as expected from analytical Chern number calculations. Moving forward, we explore the...
The probability distribution effectively sampled by a complex Langevin process for theories with a sign problem is not known a priori and notoriously hard to understand. Diffusion models, a class of generative AI, can learn distributions from data. In this contribution, we explore the ability of diffusion models to learn the distributions created by a complex Langevin process.
Understanding nonperturbative regimes in Strong-Field Quantum Electrodynamics (SFQED) is essential for exploring fundamental processes in high-intensity laser-matter interactions. Despite significant progress in analyzing the Schwinger model, a systematic comparison of the underlying frameworks remains incomplete. In particular, direct contrasts between U(1) and Zₙ models within standard...
Real-time quantum field theories remain challenging due to the severity of the numerical sign problem. In this work, we successfully apply the complex Langevin (CL) method to SU(2) Yang-Mills theory in 3+1 dimensions. By introducing an anisotropic kernel, we stabilize simulations for real-time evolutions beyond the inverse temperature, enabling the first ab initio computations of unequal-time...
