Abstract
Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining N\'eel state to a state with coexisting N\'eel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global $SO(3)$ symmetry. The field theory has four different formulations in terms of $SU(2)$ or $U(1)$ gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining N\'eel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.
Highlights
We shall study the possibility that the orbital coupling of the applied magnetic field can drive the conventional, confining, Neel insulator to a state which has semion topological order [4] coexisting with Neel order
The phase diagram we propose for the square lattice J1-J2-Jχ antiferromagnet is summarized in Fig. 1, and the critical spin liquid is realized by the deconfined critical point at Jχ = 0 between the Neel and valence bond solid (VBS) states
We can connect the field theory L2 to the lattice antiferromagnet by viewing the latter as a theory of hard-core bosons S+ = Sx + iSy; assuming the bosons form a ν = 1/2 fractional quantum Hall state, as in the chiral spin liquid [4], we identify φ as the quasiparticle operator in the Chern-Simons-Landau-Ginzburg theory [33, 34]
Summary
Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. A strong signal is found starting from optimal doping, where the pseudogap phase ends, all the way to the insulating parent compounds These observations are quite surprising, as the insulator is expected to be a conventional Neel state, and spin-wave theory shows that this state has a much smaller thermal Hall response in an applied magnetic field than that observed [3].
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