SciPost Physics

SciPost Phys. 6, 028 (2019) · published 6 March 2019

• doi: 10.21468/SciPostPhys.6.3.028
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Abstract

We investigate the ground state phase diagram of square ice -- a U(1) lattice gauge theory in two spatial dimensions -- using gauge invariant tensor network techniques. By correlation function, Wilson loop, and entanglement diagnostics, we characterize its phases and the transitions between them, finding good agreement with previous studies. We study the entanglement properties of string excitations on top of the ground state, and provide direct evidence of the fact that the latter are described by a conformal field theory. Our results pave the way to the application of tensor network methods to confining, two-dimensional lattice gauge theories, to investigate their phase diagrams and low-lying excitations.

• Emonts et al., Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1D Z2 demonstration
  Phys. Rev. D 107, 014505 (2023) [Crossref]
• Goller et al., Jordan-Wigner composite fermion liquids in a two-dimensional quantum spin ice
  Phys. Rev. B 109, 035162 (2024) [Crossref]
• Emonts et al., Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories
  SciPost Phys. Lect. Notes, 12 (2020) [Crossref]
• Felser et al., Two-Dimensional Quantum-Link Lattice Quantum Electrodynamics at Finite Density
  Phys. Rev. X 10, 041040 (2020) [Crossref]
• Feldman et al., Superselection-resolved entanglement in lattice gauge theories: a tensor network approach
  J. High Energ. Phys. 2024, 83 (2024) [Crossref]
• Carmen Bañuls et al., Review on novel methods for lattice gauge theories
  Rep. Prog. Phys. 83, 024401 (2020) [Crossref]
• Haase et al., A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
  Quantum 5, 393 393 (2021) [Crossref]
• Montangero et al., Loop-free tensor networks for high-energy physics
  Phil. Trans. R. Soc. A. 380, 20210065 (2022) [Crossref]
• Bender et al., Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states
  Phys. Rev. Research 2, 043145 (2020) [Crossref]
• Tarabunga et al., Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids
  Phys. Rev. Lett. 129, 195301 (2022) [Crossref]
• Bañuls et al., Simulating lattice gauge theories within quantum technologies
  Eur. Phys. J. D 74, 165 (2020) [Crossref]
• Hashizume et al., Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d
  SciPost Phys. 13, 017 (2022) [Crossref]
• Wiese, From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories
  Phil. Trans. R. Soc. A. 380, 20210068 (2022) [Crossref]
• Banerjee et al., Nematic confined phases in the U(1) quantum link model on a triangular lattice: Near-term quantum computations of string dynamics on a chip
  Phys. Rev. Research 4, 023176 (2022) [Crossref]
• Cataldi et al., Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
  Quantum 5, 556 556 (2021) [Crossref]
• Kondákor et al., Crystalline phases and devil's staircase in qubit spin ice
  Phys. Rev. Research 5, 043172 (2023) [Crossref]
• Bender et al., Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1) -dimensional compact QED with dynamical fermions at finite density
  Phys. Rev. Research 5, 043128 (2023) [Crossref]
• Yan et al., Widely existing mixed phase structure of the quantum dimer model on a square lattice
  Phys. Rev. B 103, 094421 (2021) [Crossref]
• Banerjee et al., Exploring bosonic and fermionic link models on (3+1)D tubes
  Phys. Rev. Research 4, 033174 (2022) [Crossref]
• Zohar, Wilson loops and area laws in lattice gauge theory tensor networks
  Phys. Rev. Research 3, 033179 (2021) [Crossref]
• Cardarelli et al., Deconfining Disordered Phase in Two-Dimensional Quantum Link Models
  Phys. Rev. Lett. 124, 123601 (2020) [Crossref]
• Celi et al., Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays
  Phys. Rev. X 10, 021057 (2020) [Crossref]
• Rigobello et al., Entanglement generation in(1+1)DQED scattering processes
  Phys. Rev. D 104, 114501 (2021) [Crossref]
• Sau et al., Weak Universality Induced by Q=±2e Charges at the Deconfinement Transition of a ( 2+1 )-Dimensional U(1) Lattice Gauge Theory
  Phys. Rev. Lett. 130, 071901 (2023) [Crossref]
• Cui et al., Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
  J. High Energ. Phys. 2020, 160 (2020) [Crossref]