Quantum and classical simulations of emergent phenomena in one dimensional quantum field theories

Fernando Quijandría¹, Diego Blas², Oriol Pujolàs³, David Zueco^1,4

¹Instituto de Ciencia de Materiales de Aragón y Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, Zaragoza E-50012, Spain

²CERN, Theory Division, 1211 Geneva, Switzerland

³Departament de Física and IFAE, Universitat Autònoma de Barcelona, Bellatera 08193, Barcelona, Spain

⁴Fundacion ARAID, Paseo María Agustín 36, Zaragoza 50004, Spain

Consider two quantum fields in one dimension (relativistic and non-relativistic). We show that, despite each of them exhibits a different group velocity in the high-energy regime, Lorentz invariance emerges as a symmetry of the system at long wavelengths. We start with a theoretical approach of the problem. Second order perturbation theory and renormalization group techniques are used to analyze the running of the velocities with the energy scale. As the strong coupling regime becomes intractable using the standard tools of QFT, we move to a classical (numerical) simulation of the non-relativistic case. The latter is based in bosonization techniques and the continuous matrix product states formalism. Finally, we propose a quantum simulation for the relativistic case using superconducting circuits. Here the problem is modeled using transmission lines coupled non-linearly by means of Josephson junctions.