A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory

Abstract

We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and the resulting Hamiltonian can be written as a rotor model. The energy eigenvalues for this Hamiltonian are computed using the tensor formulation, and compared with perturbation theory. We find good agreement between the calculations demonstrating a smooth passage from the statistical lattice Lagrangian description to the quantum Hamiltonian description.

6 pages, 4 figures

References in corpus (9)

• Tensor renormalization group approach to 2D classical lattice models
• Quantum simulation of the universal features of the Polyakov loop
• Universal features of the Abelian Polyakov loop in 1+1 dimension
• Higher order tensor renormalization group for relativistic fermion systems
• Progress towards quantum simulating the classical O(2) model
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Lattice Gauge Theories and Spin Models
• Probing the conformal Calabrese-Cardy scaling with cold atoms
• Dual representation of lattice QCD with worldlines and worldsheets of abelian color fluxes

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