• Open Access

Two-Dimensional Quantum-Link Lattice Quantum Electrodynamics at Finite Density

Timo Felser, Pietro Silvi, Mario Collura, and Simone Montangero
Phys. Rev. X 10, 041040 – Published 25 November 2020

Abstract

We present an unconstrained tree-tensor-network approach to the study of lattice gauge theories in two spatial dimensions, showing how to perform numerical simulations of theories in the presence of fermionic matter and four-body magnetic terms, at zero and finite density, with periodic and open boundary conditions. We exploit the quantum-link representation of the gauge fields and demonstrate that a fermionic rishon representation of the quantum links allows us to efficiently handle the fermionic matter while finite densities are naturally enclosed in the tensor network description. We explicitly perform calculations for quantum electrodynamics in the spin-one quantum-link representation on lattice sizes of up to 16×16 sites, detecting and characterizing different quantum regimes. In particular, at finite density, we detect signatures of a phase separation as a function of the bare mass values at different filling densities. The presented approach can be extended straightforwardly to three spatial dimensions.

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  • Received 13 January 2020
  • Revised 13 July 2020
  • Accepted 21 September 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041040

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Timo Felser1,2,3, Pietro Silvi4,5, Mario Collura1,2,6, and Simone Montangero2,3

  • 1Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
  • 2Dipartimento di Fisica e Astronomia “G. Galilei,” Università di Padova, I-35131 Padova, Italy
  • 3Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, I-35131 Padova, Italy
  • 4Center for Quantum Physics, and Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria
  • 5Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck, Austria
  • 6SISSA-International School for Advanced Studies, I-34136 Trieste, Italy

Popular Summary

Solving interacting quantum field theories, from quantum chromodynamics to the standard model, is a fundamental goal of modern physics. However, the complexity of evaluating, and thus predicting, phenomena in systems of many interacting particles from these field theories stretches beyond the power of the most advanced analytical and numerical tools available. Here, we attempt to reduce this gap by showing how one powerful mathematical tool can provide a computational tractable description of low-energy behavior in quantum electrodynamics.

Tensor networks, complex data structures developed in the last decades for the study of many-body quantum systems on a lattice, have shown great potential in addressing quantum gauge theories on 1D lattices. In this work, we study a lattice gauge theory approximating the low-energy behavior of quantum electrodynamics by means of a tree tensor network, demonstrating the successful applicability of tensor network methods in 2D gauge theories. We account for the presence of matter beside the quantum gauge fields and allow a finite charge density of the described universe, a scenario that has escaped the most advanced numerical tools.

Our results thus help bring current capabilities of tensor methods closer to the ultimate goal of fully understanding the standard model.

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Vol. 10, Iss. 4 — October - December 2020

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