Floating phase versus chiral transition in 1D constrained models - - PowerPoint PPT Presentation

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Floating phase versus chiral transition in 1D constrained models - - PowerPoint PPT Presentation

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Floating phase versus chiral transition in 1D constrained models Natalia Chepiga Swiss National Science Foundation University of Amsterdam, The Netherlands 31 July 2019 in collaboration with Fr ed eric Mila, EPFL Natalia Chepiga

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Floating phase versus chiral transition in 1D constrained models

Natalia Chepiga

Swiss National Science Foundation University of Amsterdam, The Netherlands

31 July 2019

in collaboration with Fr´ ed´ eric Mila, EPFL

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 1 / 43

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Scope

Introduction & Motivation Rigorous mapping between constrained models in 1D

Quantum dimer Quantum loop Hard bosons Fibonacci anyons

Implementation of a local constraint into DMRG Phase diagram

Floating phase vs chiral transition Ising transition Tricritical Ising. Boundary-field correspondence (conformal towers)

Outlook

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 2 / 43

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Introduction to Quantum Dimer Model (QDM)

Spin model Spin d.o.f. are located in the nodes of the lattice H = J1

  • i

Si · Si+1 Ground state: singlet Each spin-1/2 belongs to

  • ne and only one VBS

Quantum dimer model Dimer d.o.f. are associated with the bonds of original lattice QDM constraints: No free nodes No corner-sharing dimers

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 3 / 43

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QDM constraint

  • 1. Every lattice node belongs to one and only one dimer
  • 2. Only nearest neighbors bonds can be occupied by a dimer

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 3 / 43

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SLIDE 5

Introduction to Quantum Dimer Model (QDM)

Spin model Spin d.o.f. are located in the nodes of the lattice H = J1

  • i

Si · Si+1 Ground state: singlet Each spin-1/2 belongs to

  • ne and only one VBS

Number of particles: 2Nr Hilbert space: 22Nr Quantum dimer model Dimer d.o.f. are associated with the bonds of original lattice QDM constraints: No free nodes No corner-sharing dimers Number of particles: 3Nr − 2 Hilbert space: F(Nr)

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 4 / 43

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The Hilbert space

The size of the Hilbert space = the number of dimer coverings

= + + + N N-1 N-2

H(N) = H(N − 1) + H(N − 2) H(N) ≡ F(N)

Martin-Delgado, Sierra, PRL 56, ’97

Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 4 / 43