The curvature of the chiral pseudocritical line from LQCD: analytic continuation and Taylor expansion compared

We present a determination of the curvature $\kappa$ of the chiral pseudocritical line from $N_f=2+1$ lattice QCD at the physical point obtained by adopting the Taylor expansion approach. Numerical simulations performed at three lattice spacings lead to a continuum extrapolated curvature $\kappa = 0.0145(25)$, a value that is in excellent agreement with continuum limit estimates obtained via analytic continuation within the same discretization scheme, $\kappa = 0.0135(20)$. The agreement between the two calculations is a solid consistency check for both methods.Comment: Quark Matter 201

On the Lefschetz thimbles structure of the Thirring model

The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the integrals so that on each thimble the sign problem disappears. However, for systems in which more than one thimble contribute one is faced with the challenging task of collecting contributions coming from multiple thimbles. The Thirring model is a nice playground to test multi-thimble integration techniques; even in a low dimensional theory, the thimble structure can be rich. It has been shown since a few years that collecting the contribution of the dominant thimble is not enough to capture the full content of the theory. We report preliminary results on reconstructing the complete results from multiple thimble simulations.Comment: 7 pages, 5 figures, Proceedings of the 37th Annual International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, Chin

One-thimble regularisation of lattice field theories: is it only a dream?

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble.Comment: 7 pages, 1 figure, Proceedings of the 37th Annual International Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, Chin

Curvature of the pseudocritical line in QCD: Taylor expansion matches analytic continuation

We determine the curvature of the pseudo-critical line of $N_f = 2 + 1$ QCD with physical quark masses via Taylor expansion in the quark chemical potentials. We adopt a discretization based on stout improved staggered fermions and the tree level Symanzik gauge action; the location of the pseudocritical temperature is based on chiral symmetry restoration. Simulations are performed on lattices with different temporal extent ($N_t = 6, 8, 10$), leading to a continuum extrapolated curvature $\kappa = 0.0145(25)$, which is in very good agreement with the continuum extrapolation obtained via analytic continuation and the same discretization, $\kappa = 0.0135(20)$. This result eliminates the possible tension emerging when comparing analytic continuation with earlier results obtained via Taylor expansion.Comment: 11 pages, 7 figure

Quantum Computation of Thermal Averages for a Non-Abelian D4D_4 Lattice Gauge Theory via Quantum Metropolis Sampling

In this paper, we show the application of the Quantum Metropolis Sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group $D_4$ in (2+1)-dimensions, discussing in general how some components of hybrid quantum-classical algorithms should be adapted in the case of gauge theories. In particular, we discuss the construction of random unitary operators which preserve gauge invariance and act transitively on the physical Hilbert space, constituting an ergodic set of quantum Metropolis moves between gauge invariant eigenspaces, and introduce a protocol for gauge invariant measurements. Furthermore, we show how a finite resolution in the energy measurements distorts the energy and plaquette distribution measured via QMS, and propose a heuristic model that takes into account part of the deviations between numerical results and exact analytical results, whose discrepancy tends to vanish by increasing the number of qubits used for the energy measurements.Comment: 19 pages, 21 figure

Quantum Algorithms for the computation of quantum thermal averages at work

Recently, a variety of quantum algorithms have been devised to estimate thermal averages on a genuine quantum processor. In this paper, we consider the practical implementation of the so-called Quantum-Quantum Metropolis algorithm. As a testbed for this purpose, we simulate a basic system of three frustrated quantum spins and discuss its systematics, also in comparison with the Quantum Metropolis Sampling algorithm.Comment: 12 pages, 9 figure

Curvature of the pseudocritical line in QCD

The curvature of the pseudocritical line has been studied through numerical simulations performed using the tree-level Symanzik gauge action and the stout-smeared staggered fermion action. The location of the phase transition has been determined from the inflection point of the chiral condensate using two renormalization prescriptions and the curvature coefficient has been calculated by Taylor expansion, using two definitions for the pseudocritical temperature: $k_1$ has been computed by defining $T_c(\mu_B)$ under the hypothesis of constant $\bar{\psi}\psi_r$ at $T_c$ (hence defining $T_c^0$ as the inflection point of $\langle \bar{\psi}\psi_r \rangle (T, \mu_B=0)$ and $T_c(\mu_B)$ by the relation $\langle \bar{\psi}\psi_r \rangle (T_c(\mu_B), \mu_B) = \langle \bar{\psi}\psi_r \rangle (T_c^0, 0)$), while $k_2$ has been computed as the actual inflection point of $\langle \bar{\psi}\psi_r \rangle$. This set-up allows to give an independent estimate for $k_B$, investigate the systematics and make a proper comparison with previous results reported in the literature

Towards Lefschetz thimbles regularization of heavy-dense QCD

At finite density, lattice simulations are hindered by the well-known sign problem: for finite chemical potentials, the QCD action becomes complex and the Boltzmann weight $e^{-S}$ cannot be interpreted as a probability distribution to determine expectation values by Monte Carlo techniques. Different workarounds have been devised to study the QCD phase diagram, but their application is mostly limited to the region of small chemical potentials. The Lefschetz thimbles method takes a new approach in which one complexifies the theory and deforms the integration paths. By integrating over Lefschetz thimbles, the imaginary part of the action is kept constant and can be factored out, while $e^{-Re(S)}$ can be interpreted as a probability measure. The method has been applied in recent years to more or less difficult problems. Here we report preliminary results on Lefschetz thimbles regularization of heavy-dense QCD. While still simple, this is a very interesting problem. It is a first look at thimbles for QCD, although in a simplified, effective version. From an algorithmic point of view, it is a nice ground to test effectiveness of techniques we developed for multi thimbles simulations.Comment: 7 pages, 3 figures, Proceedings of the 36th Annual International Symposium on Lattice Field Theory, 22-28 July 2018, East Lansing, Michigan, US

Determination of Lee-Yang edge singularities in QCD by rational approximations

Zambello K, Clarke D, Dimopoulos P, et al. Determination of Lee-Yang edge singularities in QCD by rational approximations. arXiv:2301.03952. 2023.We report updated results on the determination of Lee-Yang edge (LYE) singularities in $N_f = 2+1$ QCD using highly improved staggered quarks (HISQ) with physical masses on $N_\tau = 4, 6, 8$ lattices. The singularity structure of QCD in the complex $\mu_B$ plane is probed using conserved charges calculated at imaginary $\mu_B$. The location of the singularities is determined by studying the (uncancelled) poles of multi-point Pad\'e approximants. We show that close to the Roberge-Weiss (RW) transition, the location of the LYE singularities scales according to the $3$-$d$ $Z(2)$ universality class. By combining the new $N_\tau = 6$ data with the $N_\tau = 4$ data from our previous analysis we extract a rough estimate for the RW temperature in the continuum limit. We also discuss some preliminary results for the singularities close to the chiral phase transition obtained from simulations on $N_\tau = 6, 8$ lattices