Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm

By T. Senthil, L. Balents, S. Sachdev, Ashvin Vishwanath, Matthew Fisher. 2003

597 citations recorded by the source corpus.

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 ${Z}_{2}$ spin liquid: the critical theory has deconfined excitations interacting with an emergent $\mathrm{U}(1)$ gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/fe7acd2844b5f2707cbaa180352b59857d9beca4

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Citations in the corpus

Deconfined quantum critical points: symmetries and dualities (2017, background): “Physically the breakdown of the Landau paradigm occurs because the topological defects of either order parameter carry nontrivial quantum numbers: the Skyrmion defect of the Néel phase carries quantum numbers under lattice symmetries [4,5,54,55], and the vortex defect of the VBS phase carries spin 1”
Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “In 2 + 1 dimensions it has been studied extensively by condensed matter physicists in the context of quantum phase transitions in valence bond solids, see for example [45–48] and the references therein.”
Comments on abelian Higgs models and persistent order (2017, methodology): “For example, the case of p = 1, N = 2 in 3d describes the Néel-VBS transition [4,5] while the case of p = 1, N = 2 and θ = π in 2d describes the Haldane model with halfinteger spin [15,16].”
Holographic Quantum Matter (2016, result): “Let us first perform an explicit computation on a free CFT3: a CFT with M two-component, massless Dirac fermions, C, with Lagrangian L = Cγµ∂µC.”
Quantum Criticality Under Decoherence or Weak Measurement (2023, background): “We demonstrate that weak measurements generally render the observed quantities rather different from the bulk QCP (with certain post-selection that preserves the O(N) symmetry in the mixed state ensemble), and we may observe the exotic extraordinary-log correlation mentioned above.”
Quantum magnetism and criticality (2007, background): “However, is it possible that Aμ becomes gapless and critical in the transition from the Néel to the VBS state ? An affirmative answer to the last question would yield a most interesting U(1) spin liquid state [28, 44].”
Quantum critical transport, duality, and M-theory (2007, methodology): “Examples are (i) the superfluidinsulator transition in the boson Hubbard model at integer filling [9–11], which is described by the φ(4) field theory with O(2) symmetry, and so is controlled by the Wilson-Fisher fixed point in D = 2+1; (ii) the spin-gap paramagnet to Néel order transition of coupled”
Lectures on holographic methods for condensed matter physics (2009, background): “The claim of [9, 10] is that as the critical point is approached from the VBS phase, terms like (11) become irrelevant, the Z4 symmetry is enhanced to U(1) and the Goldstone boson becomes a massless, quantum critical, excitation.”