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.
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.
Two-dimensional quantum antiferromagnets host rich physics, including long-range ordering, high-Tc superconductivity, quantum spin-liquid behavior, topological ordering, a variety of other exotic phases, and quantum criticalities. Frustrating perturbations in antiferromagnets may give rise to strong quantum fluctuations, challenging the theoretical understanding of the many-body ground state. Here we develop a method to describe the quantum antiferromagnets using fermionic degrees of freedom. The method is based on a formally exact mapping between spin-exchange models and theories describing fermionic matter with the emergent U(1) Chern-Simons gauge field. For the planar N\'eel state, this mapping self-consistently generates the Chern-Simons superconductor mean-field ground state of introduced spinless fermions. We systematically compare the Chern-Simons superconductor state with the planar N\'eel state at the level of collective modes as well as order parameters. We reveal qualitative and quantitative correspondences between these two states. We demonstrate that such a construction using the fractionalized excitations and Chern-Simons gauge field can not only describe the N\'eel order, but can also be applied to study quantum spin liquids. Furthermore, we show that the confinement-deconfinement transitions from the N\'eel order to quantum spin liquids are signaled and characterized by the instabilities of Chern-Simons superconductors, driven by strong frustration. The results suggest observing and classifying the descendants of antiferromagnets, including other ordered states and unconventional superconductors, as well as emergent quantum spin liquids.
Deconfined quantum criticality of two-dimensional SU(2) quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP1 model with a Maxwell term in 2+1 spacetime dimensions. We introduce a new perspective on deconfined quantum criticality within a field-theoretic framework based on an expansion in powers of ε=4−d for fixed number N of complex matter fields. We show that in the allegedly weak first-order transition regime, a so-called conformal phase transition leads to a genuine deconfined quantum critical point. In such a transition, the gap vanishes when the critical point is approached from above and diverges when it is approached from below. We also find that the spin stiffness has a universal jump at the critical point.
We study a number of quantum phase transitions, which are exotic in their nature and separates non-trivial phases of matter. Since quantum fluctuations, which drive these phase transitions, are stronger in low-dimensions, we concentrate on low-dimensional systems. We consider two different two-dimensional systems in this thesis and study their phase transition. \n\nFirst, we investigate a phase transition in graphene, one of the most famous two-dimensional systems in condensed matter. For a suspended bilayer graphene in ν = 0 quantum Hall regime, the conductivity data and mean-field analysis suggests a phase transition from an antiferromagnetic (AF) state to a valence bond solid (VBS) state, when perpendicular electric field is increased. This AF to VBS phase transition is reminiscent of deconfined criticality, which is a novel phase transition that cannot be explained by Landau’s theory of symmetry breaking. We show that in the strong coupling regime of bilayer graphene, the AF state is destabilized by the transverse electric field, likely resulting in a VBS state. We also consider monolayer and bilayer graphene in the large cyclotron gap limit and show that the effective action for the AF and VBS order parameters have a topological Wess-Zumino-Witten term, supporting that the phase transition observed in experiments is in the deconfined criticality class. \n\nSecond, we study the model systems of cuprate superconductor, which is effectively a two-dimensionalal system in the CuO_2 plane. The proposal that the pseudogap metal is a fractionalized Fermi liquid described by a quantum dimer model is extended using the density matrix renormalization group. Measuring the Friedel oscillations in the open boundaries reveals that the fermionic dimers have dispersion minima near (π/2,π/2), which is compatible with the Fermi arcs in photoemission. Moreover, investigating the entanglement entropy suggests that the dimer model with low fermion density is similar to the free fermion system above the Lifshitz transition. We also study the phase transition from a metal with SU(2) spin symmetry to an AF metal. By applying the functional renormalization group to the two-band spin-fermion model, we establish the existence of a strongly coupled fixed point and calculate critical exponents of the fixed point.
We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transition between two such VBS phases is studied. In some cases, an interesting second-order transition controlled by a fixed line with varying critical exponents is found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1∕2 spinon excitations emerge right at the transition. The low-energy physics of this critical point (up to marginally irrelevant interactions) contains just a free quadratically dispersing ``photon.'' The phase structure on one side of this continuous transition is very intricate, consisting of a series of infinitely closely spaced further transitions in a ``devil's staircase'' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a nongeneric multicritical point.
In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard ``$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$'' noncollinear antiferromagnetic order (or the so-called ${120}^{\ensuremath{\circ}}$ state) and the ``$\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$'' valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the ``intertwinement'' between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ antiferromagnetic order and the $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3d bosonic symmetry- protected topological state with only on-site symmetries.
We present the critical theory of a number of zero-temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S=1∕2 square lattice antiferromagnet between the N\'eel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second-order quantum phase transition. This conflicts with Landau-Ginzburg-Wilson theory, which predicts that such states with distinct broken symmetries are generically separated either by a first-order transition, or by a phase with co-existing orders. The critical theory of the second-order transition is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.