String-net condensation: A physical mechanism for topological phases

Levin, Michael; Wen, Xiao-Gang

doi:10.1103/physrevb.71.045110

Cited by 1,182 publications

(1,961 citation statements)

References 47 publications

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“…Levin and Wen derived the most general form of wave functions that are represented as condensation of 125122-2 stringlike extended objects on a two-dimensional lattice by further assuming that wave functions possess scale invariance and correspond to fixed points of renormalization group (RG) transformations. 15 Indeed, a ground state of Z 2 spin liquid has scale invariance as it is a superposition of loops of all the different sizes and shapes. Note that scale invariance is required for systems described by TQFT since they must be invariant under continuous deformations.…”

Section: A Topological Spin Liquid and String Netsmentioning

confidence: 99%

“…This is in strong contrast with the fact that continuous geometries often have physical interpretations based on conservation laws associated with underlying gauge symmetries as in the case of TQFT. 15 Charge conservation in scale-invariant spin models originates from group theoretical constraints imposed on the parent Hamiltonian. Fractal geometries obey a more general form of symmetries, which are referred to as algebraic symmetries in this paper, due to a possible relation to the theory of algebraic geometry which concerns geometric structures of solutions of polynomial equations.…”

Section: Another Interesting Example Of Fractal Geometries Is Generatmentioning

confidence: 99%

“…A fairly complete class of two-dimensional TQFT-based spin systems with nonchiral topological order has been proposed by Levin and Wen where condensation of highly fluctuating extended objects, called "string nets," are found to be responsible for emergence of topological order. 15 Yet, in some cases, quantum spin liquids may exhibit topological order that is beyond description of TQFT. For example, in three spatial dimensions, the cubic code, recently proposed by Haah,16 possesses topological order with stability against local perturbations, but are completely different from conventional topological spin liquids.…”

Section: Introductionmentioning

confidence: 99%

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Exotic topological order in fractal spin liquids

2013

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We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of stringlike extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.

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Section: A Topological Spin Liquid and String Netsmentioning

confidence: 99%

Section: Another Interesting Example Of Fractal Geometries Is Generatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exotic topological order in fractal spin liquids

2013

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“…Many distinct QSL states have been proposed theoretically [3,4] and classified according to their nonlocal (topological) properties [5]. Their detection, however, remains a central challenge for condensed matter physics [6], and relies on the presence of quantum entanglement in their ground state and fractional quasiparticles in their excitation spectra.…”

Section: Introductionmentioning

confidence: 99%

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO4

et al. 2018

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The spin-1=2 triangular lattice antiferromagnet YbMgGaO 4 has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of YbMgGaO 4 to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged g factors and exchange interactions. Our results paint YbMgGaO 4 as an easy-plane XXZ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained g factors are substantially different from previous reports. This work establishes the hierarchy of exchange interactions in YbMgGaO 4 from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.

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“…It has been found that the repulsive entropic force leads to a strong suppression of charmonium states near the deconfinement transition. The leading role of the entropic force in the deconfinement transition itself has been conjectured [10], as well as a possible relation of the observed peak in the entropy near the deconfinement transition to the "long string" condensation [19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Entropic destruction of heavy quarkonium in non-Abelian plasma from holography

Hashimoto

Kharzeev

2014

Phys. Rev. D

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Lattice QCD indicates a large amount of entropy associated with the heavy quark-antiquark pair immersed in the quark-gluon plasma. This entropy grows as a function of the inter-quark distance giving rise to an entropic force that can be very effective in dissociating the bound quarkonium states. In addition, the lattice data show a very sharp peak in the heavy quark-antiquark entropy at the deconfinement transition. Since the quark-gluon plasma around the deconfinement transition is strongly coupled, we employ the holographic correspondence to study the entropy associated with the heavy quark-antiquark pair in two theories: i) N = 4 supersymmetric Yang-Mills and ii) a confining Yang-Mills theory obtained by compactification on a Kaluza-Klein circle. In both cases we find the entropy growing with the inter-quark distance and evaluate the effect of the corresponding entropic forces. In the case ii), we find a sharp peak in the entropy near the deconfinement transition, in agreement with the lattice QCD results. This peak in our holographic description arises because the heavy quark pair acts as an eyewitness to the black hole formation in the bulk -the process that describes the deconfinement transition. In terms of the boundary theory, this entropy likely emerges from the entanglement of a "long string" connecting the quark and antiquark with the rest of the system.

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String-net condensation: A physical mechanism for topological phases

Cited by 1,182 publications

References 47 publications

Exotic topological order in fractal spin liquids

Exotic topological order in fractal spin liquids

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO4

Entropic destruction of heavy quarkonium in non-Abelian plasma from holography

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