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Register a new userQuantum simulation of the universal features of the Polyakov loop
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Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is a prime candidate for an experimental quantum simulation of a lattice gauge theory. To this end, we use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. The eigenstates of the Hamiltonian are neutral for periodic boundary conditions, but we probe the nonzero charge sectors by either introducing a Polyakov loop or an external electric field. In both cases we obtain universal functions relating the mass gap, the gauge coupling, and the spatial size which are invariant under the deformation of the temporal lattice spacing. We propose to use a physical multi-leg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and check the universal features. Our results provide a path to the analog quantum simulation of lattice gauge theories with atoms in optical lattices.
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We show that the Polyakov loop of the two-dimensional lattice Abelian Higgs model can be calculated using the tensor renormalization group approach. We check the accuracy of the results using standard Monte Carlo simulations. We show that the energy gap produced by the insertion of the Polyakov loop obeys universal finite-size scaling which persists in the time continuum limit. We briefly discuss the relevance of these results for quantum simulations.
The Polyakov loop of an operator in the anti-symmetric representation in N=4 SYM theory on spacial R^3 is calculated, to leading order in 1/N and at large t Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity model. Agreement is found with previous results from the supergravity dual, which is given by a D5-brane in an asymptotically AdS_5 x S^5 black brane background. It is shown that the azimuth angle, at which the dual D5-brane wraps the S^5, is related to the spectral asymmetry angle in the spectral density associated with the Greens function of the impurity fermions. Much of the calculation also applies to the Polyakov loop on spacial S^3 or H^3.
Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $Delta$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $qbar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem when treated within classical computational schemes. We show how quantum algorithms completely solve the problem, and discuss how this can apply to more complex systems of physical interest, with emphasis on the possible systematics and on their control.
Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of one such effective Polyakov loop model at finite baryon density are presented. We compute various local observables such as energy density, baryon density, quark condensate and describe in details the phase diagram of the model. The regions of the first order phase transition and the crossover, as well as the line of the second order phase transition, are established. We also compute several correlation functions of the Polyakov loops.
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