We show that the Néel states of two-dimensional antiferromagnets have low energy vector boson excitations in the vicinity of deconfined quantum critical points. We compute the universal damping of these excitations arising from spin-wave emission. Detection of such a vector boson will demonstrate the existence of emergent topological gauge excitations in a quantum spin system.
We show that the Néel states of two-dimensional antiferromagnets have low energy vector boson excitations in the vicinity of deconfined quantum critical points. We compute the universal damping of these excitations arising from spin-wave emission. Detection of such a vector boson will demonstrate the existence of emergent topological gauge excitations in a quantum spin system.
Two-dimensional quantum antiferromagnets are believed to host phases of matter whose excitations are more fundamental than those of the ordered phases. When combining two such spin systems in a bilayer, strong interaction between the emergent excitations can produce phases not realized in either of its subsystems. We show that the critical fluctuations of a two-dimensional spin-liquid state can induce a deconfined quantum critical point in a proximate antiferromagnet. The most relevant coupling between the associated effective field theories is given by a mixed Chern-Simons term of the emergent gauge fields in each layer. This describes a topological current-current interaction. In contrast to the local spin-spin interaction, it strongly modifies the renormalization group flow of the theory describing the N\'eel--valence-bond-solid transition of the antiferromagnet. In particular, the protected coupling constant associated with it implies nontrivial quantum critical scaling characterized by a nonuniversal power-law divergence of the correlation length in the critical domain and Berezinskii-Kosterlitz-Thouless divergence approaching it.
Deconfined quantum critical points are characterized by the presence of an emergent gauge field and exotic fractionalized particles, which exist as well-defined excitations only at the critical point. We here demonstrate the existence of quantum critical points described by an emergent tensor gauge theory featuring subdimensional excitations, in close relation to fracton theories. We begin by reexamining a previously studied deconfined quantum critical point between two valence bond solid (VBS) phases on a bilayer honeycomb lattice. We show that the critical theory maps onto a rank-two tensor gauge theory featuring one-dimensional particles. In a slightly different context, the same tensor gauge theory also describes a deconfined quantum critical point between a two-dimensional superfluid and a finite-momentum Bose condensate, both of which are dual to rank-one gauge theories. This represents an entirely new class of deconfined quantum criticality, in which a critical tensor gauge theory arises on top of a stable conventional gauge theory. Furthermore, we propose that this quantum critical point gives rise to a new finite-temperature phase of bosons, behaving as an Bose condensate, in which excitons (boson-hole pairs) are condensed but individual bosons are not. We discuss how small modifications of this theory give rise to the stable quantum exciton Bose liquid phase studied by Paramekanti, Balents, and Fisher.
Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP 1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry.Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z 2 topological order possibly intertwined with discrete broken global symmetries.We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette.Fluctuations about this π-flux state are described by (2 þ 1)-dimensional quantum chromodynamics (QCD 3 ) with a SU(2) gauge group and N f ¼ 2 flavors of massless Dirac fermions.It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).]that this QCD 3 theory describes the Néel-VBS quantum phase transition.We introduce adjoint Higgs fields in QCD 3 and obtain fermionic dual descriptions of the phases with Z 2 topological order obtained earlier using the bosonic CP 1 theory.We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state.The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.
We consider the quantum phase transition between a Néel antiferromagnet and a valence-bond solid (VBS) in a two-dimensional system of S = 1/2 spins. Assuming that the excitations of the critical ground state are linearly dispersing deconfined spinons obeying Bose statistics, we derive expressions for the specific heat C and the magnetic susceptibility χ at low temperature T in terms of a correlation length ξ(T). Comparing with quantum Monte Carlo results for the J-Q model, which is a candidate for a deconfined Néel-VBS transition, we obtain an almost perfect consistency between C, χ, and ξ. The corresponding expressions for magnon (triplet) excitations are not internally consistent, however, lending strong support for spinon excitations in the J-Q model.
Deconfined quantum critical points are characterized by the presence of an emergent gauge field and exotic fractionalized particles, which exist as well-defined excitations only at the critical point. We here demonstrate the existence of quantum critical points described by an emergent tensor gauge theory featuring subdimensional excitations, in close relation to fracton theories. We begin by reexamining a previously studied Lifshitz transition between two valence bond solid (VBS) phases on a bilayer honeycomb lattice. We show that the critical theory maps onto a rank-2 tensor gauge theory featuring one-dimensional particles. In a slightly different context, the same tensor gauge theory also describes a Lifshitz quantum critical point between a two-dimensional superfluid and a finite-momentum Bose condensate, both of which are dual to rank-1 gauge theories. This represents an entirely new class of deconfined quantum criticality, in which a critical tensor gauge theory arises on top of a stable conventional gauge theory. Furthermore, we propose that this quantum critical point gives rise to a new finite-temperature phase of bosons, behaving as an exciton Bose condensate, in which excitons (boson-hole pairs) are condensed but individual bosons are not. We discuss how small modifications of this theory give rise to the stable quantum ``exciton Bose liquid'' phase studied in Paramekanti, Balents, and Fisher, Phys. Rev. B 66, 054526 (2002).
We study the level structure of excitations at the ``deconfined'' critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J\text{\ensuremath{-}}Q$ model as an example. Energy gaps in different spin (S) and momentum (k) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at $\mathbf{k}=(0,0),(\ensuremath{\pi},0),(0,\ensuremath{\pi})$, and $(\ensuremath{\pi},\ensuremath{\pi})$, as inferred from two-spinon excitations (S=0 and S=1 states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).