In this thesis we explore numerical simulations, including Tensor Networks (TNs) methods, to study Hamiltonian Lattice Gauge Theories (LGTs), a numerical framework for investigating nonperturbative properties of Quantum Field Theories. We develop a modelindependent approach for constructing Matrix Product Operators (MPOs) representations of 1dimensional quasiparticles with definite momenta, and apply it to Hamiltonian Lattice Quantum Electrodynamics (QED) on a ladder geometry. By means of exact diagonalization at intermediate system sizes, we obtain the first excitation band states (the Bloch functions) representing the single(quasi)particle states (the photons) expressed as entangled states of local lattice gauge fields. We then construct the corresponding maximallylocalized Wannier functions through minimization of a spread functional. Once we identify, via a linear algebra problem, the operation that constructs the localized Wannier excitation from the ground state (dressed vacuum), we can express the creation operator, for any wavepacket of such quasiparticles, as a Matrix Product Operator. The aforementioned steps constitute a constructive strategy to prepare an arbitrary input state for a quasiparticle scattering simulation in real time, and the scattering process itself can be carried out with any standard algorithm for timeevolution with Matrix Product States.
In this thesis we explore numerical simulations, including Tensor Networks (TNs) methods, to study Hamiltonian Lattice Gauge Theories (LGTs), a numerical framework for investigating nonperturbative properties of Quantum Field Theories. We develop a modelindependent approach for constructing Matrix Product Operators (MPOs) representations of 1dimensional quasiparticles with definite momenta, and apply it to Hamiltonian Lattice Quantum Electrodynamics (QED) on a ladder geometry. By means of exact diagonalization at intermediate system sizes, we obtain the first excitation band states (the Bloch functions) representing the single(quasi)particle states (the photons) expressed as entangled states of local lattice gauge fields. We then construct the corresponding maximallylocalized Wannier functions through minimization of a spread functional. Once we identify, via a linear algebra problem, the operation that constructs the localized Wannier excitation from the ground state (dressed vacuum), we can express the creation operator, for any wavepacket of such quasiparticles, as a Matrix Product Operator. The aforementioned steps constitute a constructive strategy to prepare an arbitrary input state for a quasiparticle scattering simulation in real time, and the scattering process itself can be carried out with any standard algorithm for timeevolution with Matrix Product States.
Lattice QED photonic wavepackets on ladder geometries
MORGAVI, MATTIA
2022/2023
Abstract
In this thesis we explore numerical simulations, including Tensor Networks (TNs) methods, to study Hamiltonian Lattice Gauge Theories (LGTs), a numerical framework for investigating nonperturbative properties of Quantum Field Theories. We develop a modelindependent approach for constructing Matrix Product Operators (MPOs) representations of 1dimensional quasiparticles with definite momenta, and apply it to Hamiltonian Lattice Quantum Electrodynamics (QED) on a ladder geometry. By means of exact diagonalization at intermediate system sizes, we obtain the first excitation band states (the Bloch functions) representing the single(quasi)particle states (the photons) expressed as entangled states of local lattice gauge fields. We then construct the corresponding maximallylocalized Wannier functions through minimization of a spread functional. Once we identify, via a linear algebra problem, the operation that constructs the localized Wannier excitation from the ground state (dressed vacuum), we can express the creation operator, for any wavepacket of such quasiparticles, as a Matrix Product Operator. The aforementioned steps constitute a constructive strategy to prepare an arbitrary input state for a quasiparticle scattering simulation in real time, and the scattering process itself can be carried out with any standard algorithm for timeevolution with Matrix Product States.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/51898