Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice

Zhang, Xuefeng; He, Yin-Chen; Eggert, Sebastian; Moessner, Roderich; Pollmann, Frank

doi:10.1103/physrevlett.120.115702

Cited by 57 publications

(45 citation statements)

References 64 publications

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“…This transition in the case of full SU(2) symmetry of the Hamiltonian has been realized by the J-Q and related models, and these have been extensively simulated numerically using unbiased QMC techniques [28,32,[53][54][55][56][57][58][59][60][61][62]. Although there are studies that indicate that some version of the J-Q model with an inplane spin symmetry and other Uð1Þ symmetric models should lead to a first-order transition [35][36][37][38], in this work we demonstrate that a different model, the EPJQ model, instead leads to a continuous transition in some regions of its parameter space (we also note there is a recent QMC work on the extended Hubbard model of hard-core bosons on the kagome lattice, suggesting a similar continuous easy-plane phase transition [63], consistent with our finding here). The r and h terms in Eq.…”

Section: Lattice Modelssupporting

confidence: 66%

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

et al. 2017

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Recently, significant progress has been made in (2 þ 1)-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities; i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly correlated quantum-matter systems: the one relating the easy-plane noncompact CP 1 model (NCCP 1 ) and noncompact quantum electrodynamics (QED) with two flavors (N ¼ 2) of massless two-component Dirac fermions. The easyplane NCCP 1 model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while N ¼ 2 noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work, we present strong numerical support for the proposed duality. We realize the N ¼ 2 noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC simulations, we study a planar version of the S ¼ 1=2 J-Q spin Hamiltonian (a quantum XY model with additional multispin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships. In the J-Q model, we find both continuous and first-order transitions, depending on the degree of planar anisotropy, with deconfined quantum criticality surviving only up to moderate strengths of the anisotropy. This explains previous claims of no deconfined quantum criticality in planar two-component spin models, which were in the stronganisotropy regime, and opens doors to further investigations of the global phase diagram of systems hosting deconfined quantum-critical points.

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Section: Lattice Modelssupporting

confidence: 66%

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

et al. 2017

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“…Some of these dualities can be explicitly derived within a lattice formulation [22], others follow perturbing established supersymmetric dualities [23], or can be verified in the large-N limit [24]. Numerical evidence for the proposed duality between the easy-plane CP 1 sigma model and QED 3 has been purported very recently as well [7,9].…”

Section: Introductionmentioning

confidence: 93%

Deconfined criticality from the QED3 -Gross-Neveu model at three loops

et al. 2018

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The QED3-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Néel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED3-Gross-Neveu model by means of an expansion around the upper critical space-time dimension of D + c = 4 up to the three-loop order. Estimates for critical exponents in 2 + 1 dimensions are obtained by evaluating the different Padé approximants of their series expansion in . We find that these estimates, within the spread of the Padé approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED3-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2 < D < 4. arXiv:1807.04958v2 [cond-mat.str-el]

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“…9 A series of numerical studies of 2D lattice models that were designed with the potential to host deconfined quantum criticality, have been performed. [14][15][16][17][18][19][20][21][22][23][24][25][26] However, confirming numerically the existence of deconfined quantum criticality has been a hard task. First, one must identify the proper two-dimensional lattice model that may host a direct continuous quantum phase transition between two phases that break spontaneously and in distinct ways the symmetries of the lattice Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

et al. 2019

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The phase diagram of the quantum spin-1/2 antiferromagnetic J 1 -J 2 XXZ chain was obtained by Haldane using bosonization techniques in Refs. 1 and 2. It supports three distinct phases for 0 ≤ J 2 /J 1 < 1/2, i.e., a gapless algebraic spin liquid phase, a gapped long-range ordered Neel phase, and a gapped long-range ordered dimer phase. Even though the Neel and dimer phases are not related hierarchically by a pattern of symmetry breaking, it was shown that they meet along a line of quantum critical points with a U(1) symmetry and central charge c = 1. Here, we extend the analysis made by Haldane on the quantum spin-1/2 antiferromagnetic J 1 -J 2 XYZ chain using both bosonization and numerical techniques. We show that there are three Neel phases and the dimer phase that are separated from each other by six planes of phase boundaries realizing Gaussian criticality when 0 ≤ J 2 /J 1 < 1/2. We also show that each long-range ordered phase harbors topological point defects (domain walls) that are dual to those across the phase boundary in that a defect in one ordered phase locally binds the other type of order around its core. By using the bosonization approach, we identify the critical theory that describes simultaneous proliferation of these dual point defects, and show that it supports an emergent U(1) symmetry that originates from the discrete symmetries of the XYZ model. To confirm this numerically, we perform exact diagonalization and density-matrix renormalization-group calculations and show that the critical theory is characterized by the central charge c = 1 with critical exponents that are consistent with those obtained from the bosonization approach. Furthermore, we generalize the field theoretic description of direct continuous phase transition to higher dimensions, especially in d = 3, by using a non-linear sigma model (NLSM) with a topological term. In particular, we propose the π-flux phase on the cubic lattice with local quartic interactions as a platform for direct continuous phase transition and deconfined criticality. We discuss possible phase diagrams for the π-flux phase on the cubic lattice with these quartic interactions from the renormalization flow of NLSMs. CONTENTS

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Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice

Cited by 57 publications

References 64 publications

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

Deconfined criticality from the QED3 -Gross-Neveu model at three loops

Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

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