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, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here 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.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-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations 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 the 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 ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.
Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (
2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (
Nf) and the strength of gauge fluctuations is mapped out. Here we focus on the large fermion flavor case (
Nf=8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the
QED3-Gross-Neveu chiral O(2) universality whose properties are still largely unknown.
The problem of a U(1) U ( 1 ) gauge field coupled to fermions in (2+1) dimensions is of fundamental importance, as it is believed to give rise to U(1) U ( 1 ) Dirac spin liquid (DSL) state in quantum magnets and the strongly coupled conformal field theory in quantum electrodynamics. However, numerical progress has long been hampered by the steep computational cost of traditional determinant quantum Monte Carlo (QMC). Here, we develop a GPU-accelerated hybrid QMC algorithm assisted with several novel technical improvements, which significantly reduces the complexity to be linear with respect to space-time volume, and scales the simulation up to an unprecedented size. At this scale, we observe asymptotic convergence of fermion bilinear correlator and conserved current correlator, which was unclear previously, and find their scaling dimensions in good agreement with field theory, which supports the conformal nature of the Dirac spin liquid. Our advances establish a scalable framework to study DSL physics and its transitions at larger scales.