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Register a new userConformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
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We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e. a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$ QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion bilinear operator. We bootstrap their single correlators as well as the mixed correlators between them. We first discuss the bootstrap kinks from single correlators. Some exponents of these bootstrap kinks are close to the expected values of QED$_3$, but we provide clear evidence that they should not be identified as the QED$_3$. We then provide rigorous numerical bounds for the Dirac spin liquid and the $N=7$ Stiefel liquid to be stable critical phases on the triangular and kagome lattice. For the triangular and kagome Dirac spin liquid, the rigorous lower bounds of the monopole operators scaling dimension are $1.046$ and $1.105$, respectively. These bounds are consistent with the latest Monte Carlo results.
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We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.
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Fascinating new phases of matter can emerge from strong electron interactions in solids. In recent years, a new exotic class of many-body phases, described by generalized electromagnetism of symmetric rank-2 electric and magnetic fields and immobile charge excitations dubbed fractons, has attracted wide attention. Beside interesting properties in their own right, they are also closely related to gapped fracton quantum orders, new phases of dipole-coversing systems, quantum information, and quantum gravity. However, experimental realization of the rank-2 U(1) gauge theory is still absent, and even known practical experimental routes are scarce. In this work we propose a scheme of coupled optical phonons and nematics as well as several of its concrete experimental constructions. They can realize the electrostatics sector of the rank-2 U(1) gauge theory. A great advantage of our scheme is that it requires only basic ingredients of phonon and nematic physics, hence can be applied to a wide range of nematic matters from liquid crystals to electron orbitals. We expect this work will provide crucial guidance for the realization of rank-2 U(1) and fracton states of matter on a variety of platforms.
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