Vison states and confinement transitions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>spin liquids on the kagome lattice

Huh, Young Eun; Punk, Matthias; Sachdev, Subir

doi:10.1103/physrevb.84.094419

Cited by 77 publications

(124 citation statements)

References 56 publications

(97 reference statements)

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“…In particular, the nature of the ground state of the pure kagome Heisenberg antiferromagnet (i.e., at J 2 = 0,J 1 > 0) is still debated. Several valence bond crystals [34][35][36][37][38][39][40] and spin liquid ground states [41][42][43][44][45][46][47][48][49][50][51][52][53] (both gapless and gapped) have been proposed. Remarkably, recent state-ofthe-art DMRG calculations have provided robust evidence of a gapped Z 2 topological spin liquid.…”

Section: Models and Methodsmentioning

confidence: 99%

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

et al. 2013

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In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J 1 -J 2 Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J 2 , the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.

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Section: Models and Methodsmentioning

confidence: 99%

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

et al. 2013

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“…Despite substantial analytical and numerical effort, no agreement has been reached yet in the community. The proposed ground states include several valence bond crystals (VBCs) [1][2][3][4][5][6][7], and both gapped and gapless spin liquids [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

et al. 2015

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We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-1/2 J 1 -J 2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J 2 = 0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J 2 ≈ 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J 2 , the ground state displays signatures of the magnetic order of the √ 3 × √ 3 and the q = 0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q = 0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.

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“…In addition, quantum number fractionalizationsσ 2 = ±1 andR 6 π/3 = ±1 are listed in the last two columns of Table II. A limitation of the previous PSG analysis is that it is tied to the Schwinger-boson formalism and hence only gives the crystal symmetry fractionalization of the bosonic spinons. The vison excitation in all four states has the same crystal symmetry fractionalization [4,27]:…”

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confidence: 99%

Detecting crystal symmetry fractionalization from the ground state: Application toZ2spin liquids on the kagome lattice

2015

Phys. Rev. B

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In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different symmetry-enriched spin liquid states with identical intrinsic topological order. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected Z 2 spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of Z 2 spin liquid states on the kagome lattice. It is well known that anyons in topologically ordered phases can carry symmetry quantum numbers that are quantized to fractional values. In the celebrated example of fractional quantum Hall states, Laughlin quasiparticles carry fractional charge-the quantum number of the U (1) symmetry [1]. In recent years, great progress has been made in understanding the interplay between symmetry and fractionalization in other topologically ordered states. In particular, topological spin liquids exhibit a more subtle kind of symmetry fractionalization, associated with the crystal symmetry of the underlying lattice instead of internal symmetries [2][3][4]. While some aspects of it have been studied for quite a while, crystal symmetry fractionalization has now received renewed attention, due to an increased interest in the role of crystal symmetry in topological phases of matter. This topic is also becoming timely in view of strong numerical evidence for spin liquids on kagome lattice found in the last few years [5][6][7][8][9]. In order to fully pin down the topological nature of the numerically found spin liquid liquid, the complete pattern of crystal symmetry fractionalization needs to be determined.In this work, we offer our perspective on crystal symmetry fractionalization in Z 2 spin liquids. We find that the nontrivial way that crystal symmetry acts on an individual anyon is directly related to the symmetry representation of the topologically ordered ground states, as labeled by the crystal momentum and parity of many-body wave functions. Given that states with different symmetry labels cannot be adiabatically connected, our finding immediately makes it clear that the classification of spin liquids is refined and enriched by taking into account crystal symmetries [10]. Our theoretical result also provides a straightforward method to classify and detect different spin liquids in numerical studies. As a concrete example, we demonstrate that our method can be used to easily distinguish various Z 2 spin liquids on the kagome lattice [11][12][13].We begin by briefly reviewing what is known about crystal symmetry fractionalization in Z 2 spin liquids, and setting up the terminology for our work. A Z 2 spin liquid [14,15] supports three types of anyon excitations: bosonic spinons, fermionic spinons, and visons. ...

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Vison states and confinement transitions ofZ2spin liquids on the kagome lattice

Cited by 77 publications

References 56 publications

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

Detecting crystal symmetry fractionalization from the ground state: Application toZ2spin liquids on the kagome lattice

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