Dynamics of compact quantum electrodynamics at large fermion flavor

Abstract

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 (N f ) and the strength of gauge fluctuations is mapped out [1]. Here we focus on the large fermion flavor case (N f = 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 QED 3 -Gross-Neveu chiral O(2) universality whose properties still largely unknown.

Revealing fermionic quantum criticality from new Monte Carlo techniques

“…Importantly, we found the decaying power match perfectly with the larger-N f perturbative renormalization group expression [96,97,118,119]. The continuous confined transitions from U1D to AFM or VBS we found should be described by QED 3 -Gross-Neveu O (2) or O(3) universality, depending on the symmetry group that the fermion bilinears break in the confined phase, and further carefully study of the critical properties of these transitions via QMC simulations and analytical calculations is certainly worthwhile [93]. Recently perturbative renormalization group calculations to higher orders have been carried out in attempt to accquire the critical properties of the deconfinement to confinement transition in form of QED 3 -Gross-Neveu universality classes [120][121][122][123][124][125] and to address the relevance or irrelevance of the monopole operators to the stability of the U1D phase [126][127][128], show substantial interests and great ongoing efforts along this direction.…”

“…More interestingly, the exact form of critical bosons can even go beyond the conventional condensed matter wisdom and acquire incarnations with high-energy flavor, such that they could play the role of gauge degree of freedom and carry gauge symmetry and topological orders. In this way, the situation of matter fields couples to gauge fields can be realized in our setting and the rich physics of fractionalization of electrons to anyons coupled to the emergent gauge fields of Z 2 [88][89][90][91][92] and U(1) [46,93] symmetries in many strongly correlated systems such as Z 2 and U(1) topological orders [94][95][96][97] and their ma-terial and model realizations in quantum spin liquids [98][99][100][101][102][103] and deconfined quantum criticalities [104][105][106][107], and the fundamental question of the existence of deconfinement at (2+1)D quantum electrodynamics (QED 3 ) with fermionic matter in high-energy physics [108][109][110][111], can now be addressed with unbiased quantum Monte Carlo simulations. The development in this direction is fast and profound.…”

“…More recently, Dirac fermions coupled U(1) gauge fields problem is studied by some of us [46,93]. Our designer Hamiltonian, in the spirit of Eq.…”

Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

“…For small values of the gauge coupling, the numerical results are consistent with a gapless phase described by the deconfined, conformal QED 3 fixed point, which can be accessed either in the large-N f expansion [22][23][24][25][26] or in the ϵ expansion below four spacetime dimensions [27][28][29][30]. When the gauge coupling becomes strong, a quantum phase transition from the deconfined QED 3 phase to a confining phase occurs, accompanied by chiral symmetry breaking and dynamical mass generation for the fermions, and is found to be continuous [19][20][21]. For N f ¼ 2, the confining phase is a Néel antiferromagnet.…”

“…By contrast, stronger effects of gauge fluctuations are expected to occur for lattice gauge theories with continuous gauge groups. Recently, sign-problem-free quantum Monte Carlo (QMC) simulations of a Uð1Þ lattice gauge theory with an even number N f of flavors of fermions on the square lattice were performed [19][20][21]. At half filling, π magnetic flux is spontaneously generated in each plaquette-as in the Z 2 case-and Dirac fermions likewise emerge at low energies.…”