Quantum criticality with two length scales

Shao, Hui; Guo, Wenan; Sandvik, Anders W.

doi:10.1126/science.aad5007

Cited by 247 publications

(349 citation statements)

References 37 publications

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“…19), where a diffuse continuum of excitations exists all the way from h ¼ 0 (Z 2 Dirac phase) to h ∼ 1=3 (VBS to AFM transition). It is also worth mentioning that the system sizes with which we are working (L ≤ 16) are an order of magnitude smaller than the ones for spin [75] and loop [76] models, which exhibit deconfined quantum criticality.…”

Section: Summary and Future Directionsmentioning

confidence: 98%

Simple Fermionic Model of Deconfined Phases and Phase Transitions

2016

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Using quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with N flavors of fermions per site for N ¼ 1, 2, and 3. The models have an extensive number of conserved quantities but are not integrable, and they have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond the Landau-Ginzburg paradigm. In particular, one of the prominent phases for N > 1 corresponds to 2N gapless Dirac fermions coupled to an emergent Z 2 gauge field in its deconfined phase. However, unlike a conventional Z 2 gauge theory, we do not impose "Gauss's Law" by hand; instead, it emerges because of spontaneous symmetry breaking. Correspondingly, unlike a conventional Z 2 gauge theory in two spatial dimensions, our models have a finite-temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short-range entangled phase, which corresponds to Néel antiferromagnet or superconductor for N ¼ 2 and a valence-bond solid for N ¼ 3. Furthermore, for N ¼ 3, the valence-bond solid further undergoes a transition to a Néel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.

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Section: Summary and Future Directionsmentioning

confidence: 98%

Simple Fermionic Model of Deconfined Phases and Phase Transitions

2016

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“…This scenario was forbidden in the standard Landau's paradigm but was proposed to be possible in quantum spin systems [1,2]. 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%

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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“…Finite temperature effects are absent when β ≈ 5L for both SU(6) and SU (21). We therefore conservatively fix β = 6L for the crossing analysis and data collapse presented in the main paper.…”

Section: Measurementsmentioning

confidence: 99%

New Easy-Plane CPN−1 Fixed Points

D’Emidio

Kaul

2017

Phys. Rev. Lett.

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We study fixed points of the easy-plane CP N −1 field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N ) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N . Renormalization group calculations in 4 − dimensions provide an explanation of these results as arising due to the existence of an Nep that separates the fate of the flows with easy-plane anisotropy. When N < Nep the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for N > Nep the flows are to a new easy-plane CP N −1 fixed point that describes the quantum criticality in the lattice model at large N . Our lattice model at its critical point, thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.Introduction: The study of anti-ferromagnets has uncovered fascinating connections between quantum spin models and gauge theories. The connections have allowed novel gauge theoretic concepts such as deconfinement to be brought into the realm of condensed matter physics. Turning this mapping around, can the study of magnetism provide non-perturbative insights into gauge theories? Remarkably, advances in simulation algorithms for quantum anti-ferromagnets [1] have recently allowed controlled numerical access to otherwise poorly understood strongly coupled gauge theories; the most prominent example being the CP N −1 gauge theory proposed for deconfined critical points (DCP) in SU(N ) magnets [2].In early work on DCP, a prominent role was played by the "easy-plane SU(2)" [3] magnet and its corresponding "easy-plane CP 1 " field theory [2,4]. A self-duality in the field theory suggested that this could be the best candidate for a deconfined critical point [5]. Subsequent numerical work has concluded however that this transition is first order, both in direct discretizations of the field theory [6,7] as well as in simulations of the quantum anti-ferromagnet [8]. The easy-plane case is in contrast to the symmetric SU(N ) case (we refer to this as s-SU(N )), where striking agreement between technical field theoretic calculations [9][10][11][12] and numerical simulations of the quantum magnets has been demonstrated [13][14][15].The sharp contrast between the easy-plane and symmetric cases has been unexplained so far. In this work we address the first order transition in the easy-plane case using both lattice simulations of an ep-SU(N ) model as well as renormalization group calculations on a proposed ep-CP N −1 field theory. We find the first order transition in the ep-SU(N ) models found for N = 2 in previous work persists for larger N . A careful analysis however shows that the first order jump quantitatively weakens as N increases. Renormalization group -expansion ...

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Quantum criticality with two length scales

Cited by 247 publications

References 37 publications

Simple Fermionic Model of Deconfined Phases and Phase Transitions

Simple Fermionic Model of Deconfined Phases and Phase Transitions

Deconfined quantum critical point on the triangular lattice

New Easy-Plane CPN−1 Fixed Points

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