Position-dependent excitations and UV/IR mixing in the 
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 rank-2 toric code and its low-energy effective field theory

Pace, Salvatore D.; Wen, Xiao-Gang

doi:10.1103/physrevb.106.045145

Cited by 23 publications

(6 citation statements)

References 77 publications

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“…For example, the simplest higher-rank gauge theories feature the conservation of both charge and dipole moment, which immobilizes individual charges but allows for the motion of stable dipolar bound states. Parallel to this development, similar approaches have been proposed for understanding fractonic phases using a symmetry-gauging principle by considering certain exotic higher-form symmetries [72][73][74], subsystem symmetries [61,75,76], or global symmetries that act on quasiparticles with position-dependent charge [77][78][79].…”

Section: Prelude: Fracton and Higher-rank Gauge Theoriesmentioning

confidence: 99%

“…Under this framework, the worldlines of particles become immobile, as they are considered charged objects subject to 1-form symmetries. Through this approach, instead of identifying a special form of charge multipole symmetry and delineating its corresponding gauged theory, it allows us to identify exotic fracton liquids whose quasiparticle mobility restrictions are precisely defined by the chosen commutation relations between charges and translations [78,97]. In a parallel thread, attention has been directed towards the twisted tensor gauge theory, where the general Maxwell theory for higher-rank electromagnetic fields is enhanced by an additional Chern-Simons type coupling [30,79,[98][99][100][101][102][103].…”

Section: Rank Of Theory Local Constraint Gapless Dispersion Heat Capa...mentioning

confidence: 99%

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Emergent fractons and algebraic quantum liquid from plaquette melting transitions

You

Bi²,

Pretko

2020

Phys. Rev. Research

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Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist, can potentially inhibit the condensation of vortices and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by proliferation of spinon dipoles. For example, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization. We also study 3d valence plaquette and valence cube ordered phase, and demonstrate that the topological defects therein also have fractonic dynamics. Possible nearby phases after melting the valence plaquettes or cubes are also discussed.

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Section: Prelude: Fracton and Higher-rank Gauge Theoriesmentioning

confidence: 99%

Section: Rank Of Theory Local Constraint Gapless Dispersion Heat Capa...mentioning

confidence: 99%

Emergent fractons and algebraic quantum liquid from plaquette melting transitions

You

Bi²,

Pretko

2020

Phys. Rev. Research

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“…This procedure is contrasted with the case where the Z N topological phase (toric code) is obtained from the conventional Maxwell theory via Higgs mechanism. See [27,28,29,30] for more explanations on other types of higher rank Maxwell theories and their Higgs phases.…”

Section: Model Hamiltonianmentioning

confidence: 99%

Symmetric higher rank topological phases on generic graphs

Ebisu¹

2023

Preprint

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Motivated by recent interests in fracton topological phases, we explore interplay between gapped 2D Z N topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such phases are placed. We investigate the properties of the phases in a new geometric context -graph theory. By placing the phases on a 2D lattice consisting of two arbitrary connected graphs, G x ⊠ G y , we study the behavior of fractional excitations of the phases. We derive the formula of the ground state degeneracy of the phases, which depends on invariant factors of the Laplacian.

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“…Once we have identified the closed loops of electric charges in the x-direction, they can be deformed into the ones shifted upwards or downwards in the y-direction by applying sets of P (v i , y+1/2) , corresponding to the fusion rule (12), therefore, we have exhausted all kinds of closed loops of electric charges in the x-direction, fully labeled by (23). The explicit form of the closed loops, consisting of multiple of Z 1 operators, is obtained by multiplying the matrix Q from the left in (22). More explicitly, the closed loop of an electric charge in the x-direction, W e,x,r α is labeled by α := ( gcd(N ,p 1 ) ,…”

Section: Superselection Sectors and Gsdmentioning

confidence: 99%

“…The GSD dependence on gcd of N and length of the lattice was studied in the Wen's 2 plaquette model and several models in the case of the square lattice [21,22]. Here, by employing algebraic tools of graph theory, we have derived such novel GSD dependence in the case of an arbitrary connected graph.…”

Section: Superselection Sectors and Gsdmentioning

confidence: 99%

Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs

Ebisu

Han

2023

SciPost Phys.

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We study unusual gapped topological phases where they admit \mathbb{Z}_NℤN fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by \bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2[N×∏igcd(N,pi)]2, where p_ipi’s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.

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Position-dependent excitations and UV/IR mixing in the ZN rank-2 toric code and its low-energy effective field theory

Cited by 23 publications

References 77 publications

Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Symmetric higher rank topological phases on generic graphs

Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs

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