Deconfinement of spinons on critical points: Multiflavor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>CP</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>lattice gauge theory in three dimensions

Takashima, Shunsuke; Ichinose, Ikuo; Matsui, Tetsuo

doi:10.1103/physrevb.73.075119

Cited by 35 publications

(27 citation statements)

References 28 publications

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“…and a correlation length ξ F using Eq. (8). Of course, one can define an analogous correlation function G F (x) by considering the y or the z direction.…”

Section: B Observablesmentioning

confidence: 99%

“…Abelian U(1) gauge theories with multicomponent scalar fields, characterized by a global SU(N) symmetry, emerge as effective theories in many different physical contexts [1][2][3][4][5][6][7][8][9][10][11][12][13]. In particular, they provide an effective description of deconfined quantum critical points [14], for example, of the Néel to valence-bond-solid transition in two-dimensional antiferromagnetic SU(2) quantum systems [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Higher-charge three-dimensional compact lattice Abelian-Higgs models

2020

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We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N 2 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gaugeinvariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., N = 2 and N = 25.

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“…and a correlation length ξ F using Eq. (8). Of course, one can define an analogous correlation function G F (x) by considering the y or the z direction.…”

Section: B Observablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher-charge three-dimensional compact lattice Abelian-Higgs models

2020

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“…Models of scalar fields with U(1) gauge symmetry and SU(N) global symmetry emerge as effective theories of superconductors, superfluids, and of quantum SU(N) antiferromagnets [1][2][3][4][5][6][7][8]. In particular, three-dimensional (3D) classical U(1) gauge models with N = 2 supposedly describe the transition between the Néel and the valence-bond-solid state in two-dimensional antiferromagnetic SU(2) quantum systems [9][10][11][12][13][14][15][16] that represent the paradigmatic models for the so-called deconfined quantum criticality [17].…”

Section: Introductionmentioning

confidence: 99%

Lattice Abelian-Higgs model with noncompact gauge fields

2021

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Higgs model with noncompact gauge fields. For any N 2, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: The Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalarfield and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the phases they separate, and on the number N of components of the scalar field. In particular, the Coulombto-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson 4 theory sharing the same SU(N) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with C * boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of N, i.e., N = 2, 4, 10, 15, and 25. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for N 10, in agreement with the predictions of the Abelian-Higgs field theory.

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“…If we include N f -fold CP 1 variables, the gauge-boson mass on the critical line vanishes for N f Ն 14. 8 In Fig. 2, we show the result of our calculations of the O͑3͒ spin-spin correlation functions, C S ͑r͒ = ͗S ជ x+r · S ជ x ͘.…”

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confidence: 99%

Four-dimensionalCP1+U(1)lattice gauge theory for three-dimensional antiferromagnets: Phase structure, gauge bosons, and spin liquid

et al. 2008

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In this paper we study the lattice CP 1 model in ͑3+1͒ dimensions coupled with a dynamical compact U͑1͒ gauge field. This model is an effective field theory of the s = 1 2 antiferromagnetic Heisenberg spin model in three spatial dimensions at zero temperature. By means of Monte Carlo simulations, we investigate its phase structure. There exist the Higgs, Coulomb and confinement phases, and the parameter regions of these phases are clarified. We also measure the magnetization of O͑3͒ spins, the energy gap of spin excitations, and the mass of gauge boson. Then we discuss the relationship between these three phases and magnetic properties of the high-T c cuprates, in particular the possibility of deconfined-spinon phase. Effect of dimerlike spin exchange coupling and ring-exchange coupling is also studied.The CP N spin model plays an important role in various fields of physics not only as a tractable field-theory model that has interesting phase structure, but also as an effective field theory for certain systems in condensed matter physics and beyond. In particular, the CP 1 model corresponds to the Schwinger-boson representation of the s = 1 2 antiferromagnetic ͑AF͒ quantum spin model, i.e., the AF Heisenberg model. 1 The CP 1 model is much more tractable than the original AF Heisenberg model, and its phase structure and critical behavior have been investigated both analytically and numerically. The system intrinsically contains compact U͑1͒ gauge degrees of freedom, and their dynamics determines the low-energy excitations in AF magnet. That is, if the gauge dynamics is in the deconfined-Coulomb phase, the lowenergy excitations are the s = 1 2 spinons. On the other hand, the Higgs phase corresponds to the Néel state with a longrange AF order, and the confinement phase is a valence-bond solid ͑VBS͒ state in which spin-triplet low-energy excitations appear. Most of the previous studies exploring a possible deconfined-spin-liquid phase have considered the twodimensional ͑2D͒ ͑doped͒ AF Heisenberg model at zero temperature ͑T =0͒ or its path-integral representation, the three-dimensional ͑3D͒ CP 1 model. In these cases, the Coulomb phase may be possible if there exist a sufficient number of gapless matter fields that couple to the gauge field. 2 In the present paper, we shall consider a 4D CP 1 model coupled with a dynamical U͑1͒ gauge field. This 4D CP 1 +U͑1͒ gauge model is viewed as an effective field theory of the 3D AF Heisenberg model at T = 0. From the gaugetheoretical point of view, the deconfinement nature is enhanced in ͑3+1͒ D case because the Coulomb phase exists even in the pure 4D U͑1͒ gauge system that involves no matter fields in contrast to the pure 3D U͑1͒ gauge system that has only the confinement phase. Therefore, it is interesting to study the phase structure of this 4D CP 1 gauge model. We shall first consider the CP 1 model for the 3D AF Heisenberg model with uniform nearest-neighbor spin coupling and then the CP 1 model for the 3D AF Heisenberg model with nonuniform dimerlike coupling and ring-...

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Deconfinement of spinons on critical points: MultiflavorCP1+U(1)lattice gauge theory in three dimensions

Cited by 35 publications

References 28 publications

Higher-charge three-dimensional compact lattice Abelian-Higgs models

Higher-charge three-dimensional compact lattice Abelian-Higgs models

Lattice Abelian-Higgs model with noncompact gauge fields

Four-dimensionalCP1+U(1)lattice gauge theory for three-dimensional antiferromagnets: Phase structure, gauge bosons, and spin liquid

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