Phases of the (
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) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

Wang, Zhenjiu; Zaletel, Michael P.; Mong, Roger S. K.; Assaad, Fakher F.

doi:10.1103/physrevlett.126.045701

Cited by 50 publications

(21 citation statements)

References 31 publications

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“…This theory is dual to a SO(5) nonlinear sigma model with a Wess-Zumino-Witten term [27,54,55]. There is now significant numerical evidence that such a conformal field theory (CFT) does not exist, although there is likely a nearby 'complex' CFT [31][32][33][34][35][36][37]. This leaves open the fate of a physical model with a Hermitian Hamiltonian, such as the J 1 -J 2 antiferromagnet on the square lattice, between the Néel and VBS states.…”

Section: Discussionmentioning

confidence: 99%

“…This fermionic dual is a relativistic SU(2) gauge theory of two flavors of two-component, massless Dirac fermions carrying fundamental gauge charges: This formulation is preferred over the bosonic spinons because the massless Dirac fermions connect naturally to the gapless fermionic spinons in the Z 2 spin liquid. Recent studies [31][32][33][34] have indicated that the FIG. 1.…”

Section: Introductionmentioning

confidence: 99%

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Deconfined criticality and a gapless Z2 spin liquid in the square-lattice antiferromagnet

2021

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The theory for the vanishing of Néel order in the spin S = 1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the J 1 -J 2 model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z 2 spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the 'π -flux' phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z 2 spin liquid; on the other side of the critical point, the U(1) spin liquid (the 'staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent z = 1, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J 2 /J 1 : Néel, gapless Z 2 spin liquid, and valence bond solid.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deconfined criticality and a gapless Z2 spin liquid in the square-lattice antiferromagnet

2021

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“…Whereas, in most cases, the obtained physical quantities exhibit unusual scaling violations [9,10,13,14,[18][19][20], and it is unclear whether the observed phase transition between AFM and VBS states is continuous or weakly first-order. Different scenarios have been proposed for explaining these perplexing phenomena [23][24][25][26][27][28][29][30][31][32][33][34]. According to P. W. Anderson, a QSL state can be regarded as a resonating valence bond (RVB) state [35], or the superposition of different kinds of VBS patterns, and the translational symmetry is restored by quantum fluctuations.…”

Section: Introductionmentioning

confidence: 99%

The emergence of gapless quantum spin liquid from deconfined quantum critical point

Liu,

Hasik,

Gong

et al. 2021

Preprint

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A quantum spin liquid (QSL) is a novel phase of matter with long-range many-body quantum entanglement where localized spins are highly correlated with the vanishing of magnetic order. Such exotic quantum states typically host emergent gauge fields and fractional excitations. Here we show that a gapless QSL can naturally emerge from a deconfined quantum critical point (DQCP), which is originally proposed to describe Landau forbidden continuous phase transition between antiferromagnetic (AFM) and valence-bond solid (VBS) phases. Via large-scale tensor network simulations of a square-lattice spin-1/2 frustrated Heisenberg model, we find that a gapless QSL can gradually develop from a DQCP by tuning the couplings. Remarkably, along the phase boundaries of AFM-QSL and QSL-VBS transitions, we always observe the same correlation length exponents ν ≈ 1.0, which is intrinsically different from the one of the well known AFM-VBS DQCP transition, indicating new types of universality classes. Our results suggest a new scenario for understanding the emergence of gapless QSL from an underlying DQCP. The discovered QSL phase survives in a large region of tuning parameters and we expect its experimental realizations in solid state materials or cold atom systems.

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“…< l a t e x i t s h a 1 _ b a s e 6 4 = " 2 L T W 3 i x M 9 I H E / e 0 y K i massless Dirac fermions connect naturally to the gapless fermionic spinons in the Z 2 spin liquid. Recent studies [31][32][33][34] have indicated that the 2 fermion flavor SU(2) gauge theory does not ultimately describe a conformal field theory needed for Néel-VBS criticality, but exhibits a 'pseudocriticality' associated with a proximate fixed point at complex coupling [27,[35][36][37]. Ref.…”

mentioning

confidence: 99%

Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet

Shackleton,

Thomson,

Sachdev

2021

Preprint

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The theory for the vanishing of Néel order in the spin S = 1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the J 1 -J 2 model): a gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z 2 spin liquid with massless Dirac spinon excitations; on the other side the critical point, the SU(2) spin liquid (the 'π-flux' phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant, and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z 2 spin liquid; on the other side of the critical point, the U(1) spin liquid (the 'staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent z = 1, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J 2 /J 1 : Néel, gapless Z 2 spin liquid, and valence bond solid.

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Phases of the ( 2+1 ) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

Cited by 50 publications

References 31 publications

Deconfined criticality and a gapless Z2 spin liquid in the square-lattice antiferromagnet

Deconfined criticality and a gapless Z2 spin liquid in the square-lattice antiferromagnet

The emergence of gapless quantum spin liquid from deconfined quantum critical point

Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet

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