Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $\ensuremath{\theta}$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $\ensuremath{\theta}$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes. 

pdf/computing-the-mass-shift-of-wilson-and-staggered-fermions-in-thpq0vozw1.pdf

Computing the mass shift of Wilson and staggered fermions in the lattice Schwinger model with matrix product states

We find a simple spin Hamiltonian to describe physical states of ($2+1$)-dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation of the electric field representation at ${j}_{\mathrm{max}}=\frac{1}{2}$. The simple spin Hamiltonian contains only local products of Pauli matrices, even though Gauss's law has been completely integrated out. 

Simple Hamiltonian for quantum simulation of strongly coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:math> SU(2) lattice gauge theory on a honeycomb lattice

We evaluate the entanglement entropy and entropic function of massive two dimensional QED (Schwinger model) at finite temperature, density, and $\theta$-angle. In the strong coupling regime, the entropic function is dominated by the boson mass for large spatial intervals, and reduces to the CFT result for small spatial intervals. We also discuss the entanglement spectrum at finite temperature and a finite $\theta$-angle.

Entanglement in massive Schwinger model at finite temperature and density

We numerically study the phase structure of the two-flavor Schwinger model with matrix product states, focusing on the (1+1)-dimensional analog of the CP-violating Dashen phase in QCD. Simulating the model around the point where the positive mass of one fermion flavor corresponds to the negative mass of the other fermion flavor, we explore a regime afflicted by the sign problem for conventional Monte Carlo techniques. Our results indicate that the model undergoes a CP-violating Dashen phase transition at this point, which manifests itself in abrupt changes of the average electric field and the analog of the pion condensate in the model. Studying the scaling of the bipartite entanglement entropy as a function of the volume, we find clear indications that this transition is not of first order.

Exploring the CP-Violating Dashen Phase in the Schwinger Model with Tensor Networks

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $\theta$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $\theta$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and the electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

pdf/computing-the-mass-shift-of-wilson-and-staggered-fermions-in-3baynzq2.pdf

Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States

We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-ﬂavor Schwinger model in the presence of a chemical potential. The parametric ansatz circuit we design is capable of incorporating the symmetries of the model, present in certain parameter regimes, which allows for reducing the number of variational parameters substantially. Moreover, the ansatz circuit can be implementated on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz circuit is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices.

/pdf/exploring-the-phase-structure-of-the-multi-flavor-schwinger-1cinfqfc.pdf

Exploring the phase structure of the multi-flavor Schwinger model with quantum computing

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Exploring the phase structure of the multi-flavor Schwinger model with quantum computing