Abstract
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and N\'eel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f = 4$, our data suggests a continuous quantum phase transition between the VBS and N\'{e}el order. We also provide preliminary theoretical analysis for these quantum phase transitions.
Highlights
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics
We show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations
In this work, we succeed in performing large-scale quantum Monte Carlo (QMC) simulations on the cQED3 coupled to Nf flavor of fermions and eventually map out the phase diagram (Fig. 1) in the fermion flavor and gauge field fluctuations strength plane
Summary
Perturbative renormalization-group calculations to higher orders have recently been carried out in attempt to acquire the critical properties of the deconfinement-to-confinement transition in the form of QED3-Gross-Neveu universality classes [38,39,40,41]. Based on these considerations, in this work, we succeed in performing large-scale quantum Monte Carlo (QMC) simulations on the cQED3 coupled to Nf flavor of fermions and eventually map out the phase diagram (Fig. 1) in the fermion flavor and gauge field fluctuations strength plane.
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