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

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

“…As shown in Fig. 2 (upper panel), for g 2 m ¼ 0 the system undergoes a transition between two regimes, analogously to the (1 + 1)D and (2 + 1)D cases 25,37,47 : for large positive masses, the system approaches the bare vacuum, while for large negative masses, the system is arranged into a crystal of charges, a highly degenerate state in the semiclassical limit (t → 0) due to the exponential number of electric field configurations allowed. We track this transition by monitoring the average matter density ρ…”

“…By variationally approximating the lattice QED ground state with a TTN, we address a variety of regimes and questions inaccessible before. In the scenario with zero excess charge density, we observe that the transition between the vacuum phase and the charge-crystal phase is compatible with a second-order quantum phase transition 47 . In the limit of zero magnetic couplings, this transition occurs at negative bare masses m 0 , but as the coupling is activated, the critical point is shifted to larger, and even positive, m 0 values.…”

“…In the following, in order to obtain a representation of the gauge degrees of freedom that will be useful for constructing our TN ansatz, we employ the local mapping presented in ref. 47 (see also 97,98 ), generalizing it to the case with three spatial dimensions. This technique is related to the standard rishon formulation of QLM [99][100][101] and allows us to encode Gauss's law taking into account the anticommutation relations of the fermionic particles on the lattice.…”

“…As tailored many-body quantum state ansätze, TNs are an efficient approximate entanglement-based representation of physical states, capable of efficiently describe equilibrium properties and real-time dynamics of systems described by complex actions, where Monte Carlo simulations fail to efficiently converge 22 . TN methods have proven remarkable success in simulating LGTs in (1+1) dimensions [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] , and very recently they have shown potential in (2+1) dimensions [42][43][44][45][46][47][48][49][50] . To date, due to the lack of efficient numerical algorithms to describe high-dimensional systems via TNs, no results are available regarding the realistic scenario of LGTs in three spatial dimensions.…”

A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

“…A possible solution is to employ a Hamiltonian formulation of the underlying model. Classical Hamiltonianbased simulations using tensor network states (TNS), including fermionic projected entangled-pair states, have been successful [18][19][20][21][22][23][24][25][26][27][28], but are so far restricted to mostly one spatial dimension (for link model 2D calculations with DMRG and tree tensor network see e.g [29,30]). Consequently, there is a necessity for new approaches to both access higher dimensions and address problems where standard MCMC methods fail.…”