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

Angelides, Takis; Funcke, Lena; Jansen, Karl; Kühn, Stefan

doi:10.1103/physrevd.108.014516

Cited by 9 publications

(16 citation statements)

References 46 publications

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“…This ensures that they decouple from the theory when approaching the continuum limit [46,47]. The Wilson discretization of the of the Schwinger Hamiltonian on a lattice with N sites and spacing a reads [28,48]…”

Section: Wilson Fermionsmentioning

confidence: 99%

“…For open boundary conditions, there is no analytical prediction, and we can measure the mass shift using the approach from Ref. [28]. Moreover, Ref.…”

Section: Staggered Fermionsmentioning

confidence: 99%

“…( 13), and the ones from measuring the mass shift MS L following Ref. [28]. Hence, there are in total four combinations of the two above considerations, which are all shown in Fig.…”

Section: Continuum Extrapolations With Mpsmentioning

confidence: 99%

“…Despite its simplicity, the Schwinger model in the presence of a topological θ-term provides an example where conventional Monte Carlo methods would suffer from the sign problem. Moreover, it exhibits a rich phase structure with a first-order quantum phase transition for large enough masses at θ = π [28][29][30][31][32][33][34][35][36]. Hence, Schwinger model serves as a benchmark system for developing and testing new methods.…”

Section: Introductionmentioning

confidence: 99%

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First-Order Phase Transition of the Schwinger Model with a Quantum Computer

Angelides,

Naredi,

Crippa

et al. 2024

Preprint

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We explore the first-order phase transition in the lattice Schwinger model in the presence of a topological θ-term by means of the variational quantum eigensolver (VQE). Using two different fermion discretizations, Wilson and staggered fermions, we develop parametric ansatz circuits suitable for both discretizations, and compare their performance by simulating classically an ideal VQE optimization in the absence of noise. The states obtained by the classical simulation are then prepared on the IBM's superconducting quantum hardware. Applying state-of-the art error-mitigation methods, we show that the electric field density and particle number, observables which reveal the phase structure of the model, can be reliably obtained from the quantum hardware. To investigate the minimum system sizes required for a continuum extrapolation, we study the continuum limit using matrix product states, and compare our results to continuum mass perturbation theory. We demonstrate that taking the additive mass renormalization into account is vital for enhancing the precision that can be obtained with smaller system sizes. Furthermore, for the observables we investigate we observe universality, and both fermion discretizations produce the same continuum limit.

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Section: Wilson Fermionsmentioning

confidence: 99%

“…For open boundary conditions, there is no analytical prediction, and we can measure the mass shift using the approach from Ref. [28]. Moreover, Ref.…”

Section: Staggered Fermionsmentioning

confidence: 99%

“…( 13), and the ones from measuring the mass shift MS L following Ref. [28]. Hence, there are in total four combinations of the two above considerations, which are all shown in Fig.…”

Section: Continuum Extrapolations With Mpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

First-Order Phase Transition of the Schwinger Model with a Quantum Computer

Angelides,

Naredi,

Crippa

et al. 2024

Preprint

Self Cite

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“…Since quantum error correction is not yet possible, a set of error mitigation techniques [25,26], and algorithms [27] have been specifically designed for NISQ devices. In particular different variational quantum algorithms have been explored for the simulation of the Schwinger model [16,[28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Simulation of a Rohksar-Kivelson ladder on a NISQ device

Gupta,

Javanmard,

Osborne

et al. 2024

Preprint

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We present a quantum-classical algorithm to study the dynamics of the Rohksar-Kivelson plaquette ladder on NISQ devices. We show that complexity is largely reduced using gauge invariance, additional symmetries, and a crucial property associated to how plaquettes are blocked against ringexchange in the ladder geometry. This allows for an efficient simulation of sizable plaquette ladders with a small number of qubits, well suited for the capabilities of present NISQ devices. We illustrate the procedure for ladders with simulation of up to 8 plaquettes in an IBM-Q machine, employing scaled quantum gates.

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Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Lin,

Luo,

Yao

et al. 2024

J. High Energ. Phys.

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Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

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

Cited by 9 publications

References 46 publications

First-Order Phase Transition of the Schwinger Model with a Quantum Computer

First-Order Phase Transition of the Schwinger Model with a Quantum Computer

Simulation of a Rohksar-Kivelson ladder on a NISQ device

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

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