Deconfined Quantum Critical Points: Symmetries and Dualities

Wang, Chong; Nahum, Adam; Metlitski, Max A.; Xu, Cenke; Senthil, T.

doi:10.1103/physrevx.7.031051

Cited by 373 publications

(706 citation statements)

References 120 publications

(477 reference statements)

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“…But a complete field theory which reduces to the WZW term in the infrared is still demanded. For example, the O(5) nonlinear σ model with a WZW term at level 1 can be derived as the low-energy effective-field theory of the N = 2 QCD with the SU(2) gauge field, which has an explicit SO(5) global symmetry [25].…”

Section: Field Theory and Renormalization-group Analysismentioning

confidence: 99%

“…The analogy between the DQCP on the square lattice and a threedimensional (3D) bulk SPT state with an SO(5) symmetry was discussed in Ref. [25]. Many 3D SPT states can be constructed by decorating the defects in the system with a lower-dimensional SPT state and then proliferating the defects [50,51].…”

Section: Interpretation Of the Dqcp As The Boundary Of A Three-dimentioning

confidence: 99%

“…A lot of numerical work has been devoted to investigating the DQCP with a full spin rotation symmetry [4][5][6][7][8][9][10][11][12][13][14][15], as well as spin models with only in-plane spin symmetry [16][17][18][19]. Recently developed duality between strongly interacting QCPs in (2 + 1) dimensions have further improved our understanding of the DQCP [20][21][22][23][24][25], and the predictions made by duality have received numerical support [26,27].…”

Section: Introductionmentioning

confidence: 99%

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Deconfined quantum critical point on the triangular lattice

et al. 2018

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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 " √ 3 × √ 3" noncollinear antiferromagnetic order (or the so-called 120• state) and the " √ 12 × √ 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 √ 3 × √ 3 antiferromagnetic order and the √ 12 × √ 12 VBS order. Then using a controlled renormalizationgroup calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the N f = 4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z 4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the N f = 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.

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Section: Field Theory and Renormalization-group Analysismentioning

confidence: 99%

Section: Interpretation Of the Dqcp As The Boundary Of A Three-dimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deconfined quantum critical point on the triangular lattice

et al. 2018

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“…This line of thinking has proven to be very powerful in studying difficult problems in strong correlation physics in two space dimensions. Examples include quantum Hall systems, especially the half-filled Landau level [31,[36][37][38][39][40], interacting topological insulator surfaces [32,34,35], quantum electrodynamics in 2 + 1 dimensions [33,41], and a class of Landau-forbidden quantum phase transitions known as deconfined quantum criticality [42]. The lower dimensional dualities are also interesting on their own as nontrivial results in 2 + 1 dimensional quantum field theory [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Symmetry enriched U(1) quantum spin liquids

2018

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We classify and characterize three-dimensional U(1) quantum spin liquids [deconfined U(1) gauge theories] with global symmetries. These spin liquids have an emergent gapless photon and emergent electric/magnetic excitations (which we assume are gapped). We first discuss in great detail the case with time-reversal and SO(3) spin rotational symmetries. We find there are 15 distinct such quantum spin liquids based on the properties of bulk excitations. We show how to interpret them as gauged symmetry-protected topological states (SPTs). Some of these states possess fractional response to an external SO(3) gauge field, due to which we dub them "fractional topological paramagnets." We identify 11 other anomalous states that can be grouped into three anomaly classes. The classification is further refined by weakly coupling these quantum spin liquids to bosonic symmetry protected topological (SPT) phases with the same symmetry. This refinement does not modify the bulk excitation structure but modifies universal surface properties. Taking this refinement into account, we find there are 168 distinct such U(1) quantum spin liquids. After this warm-up, we provide a general framework to classify symmetry enriched U(1) quantum spin liquids for a large class of symmetries. As a more complex example, we discuss U(1) quantum spin liquids with time-reversal and Z 2 symmetries in detail. Based on the properties of the bulk excitations, we find there are 38 distinct such spin liquids that are anomaly-free. There are also 37 anomalous U(1) quantum spin liquids with this symmetry. Finally, we briefly discuss the classification of U(1) quantum spin liquids enriched by some other symmetries.

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“…(This connection was recently revisited in greater detail in Ref. [66]. ) We first verify that this reformulation has the required properties of the EP-NCCP1 model in terms of l 1 and l 2 .…”

Section: Connection To Self-dual Ep-nccp1 Modelmentioning

confidence: 57%

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

2017

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Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one-and two-dimensional quantum Ising models and then similarly explore the duality web of complex bosons and Dirac fermions in (2 þ 1) dimensions. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.

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Deconfined Quantum Critical Points: Symmetries and Dualities

Abstract: A. More precise Lagrangians 37 B. Some other dualities 38 C. A different view of the dualities and emergent symmetries 39 D. Some useful mathematical concepts 41 E. Topological superconductors and the APS theorem 42 References 44 arXiv:1703.02426v2 [cond-mat.str-el]

Cited by 373 publications

References 120 publications

Deconfined quantum critical point on the triangular lattice

Deconfined quantum critical point on the triangular lattice

Symmetry enriched U(1) quantum spin liquids

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

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