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 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 explicit perform calculations for quantum electrodynamics in the spin-one quantum link representation on lattice sizes of up to 16x16 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.
Highlights
Recent progress in quantum simulations is paving the way for the possibility of studying high-energy physics phenomena with tools developed in low-energy quantum physics [1,2,3,4,5,6,7,8,9,10,11,12,13]
In the Standard Model, forces are mediated through gauge fields; gauge-invariant field theories— e.g., quantum electrodynamics (QED) for the Abelian case or quantum chromodynamics (QCD) for the non-Abelian scenario—are fundamental building blocks to our understanding of all microscopic processes ruling the dynamics of elementary particles [14,15]
By exploiting the quantum-link formulation of lattice gauge theory (LGT), the fermionic rishon representation of quantum links, and unconstrained tree tensor networks, we investigated the equilibrium properties of a two-dimensional lattice QED within its first compact spin representation
Summary
Recent progress in quantum simulations is paving the way for the possibility of studying high-energy physics phenomena with tools developed in low-energy quantum physics [1,2,3,4,5,6,7,8,9,10,11,12,13]. The Monte Carlo approach suffers from the infamous sign problem for complex actions, e.g., at finite fermion density (matter-antimatter unbalance), which naturally arises in LGTs [13,24] Another very promising alternative to simulate lattice gauge theories is based on tensor network (TN) methods. We stress that the quantum-link formulation provides the ideal tools to establish a connection between LGTs and atomic lattice experiments [57,58] In this framework, the dynamical gauge fields are usually represented by spin degrees of freedom, which have a natural mapping to typical condensed-matter models, like Hubbard Hamiltonians or locally constrained Ising-like Hamiltonians. V and give additional supplementary technical details in the Appendixes
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