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

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

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

Introduction to Quantum Dimer Model (QDM) Quantum dimer model Spin model Dimer d.o.f. are associated with the Spin d.o.f. are located in bonds of original lattice the nodes of the lattice � H = J 1 S i · S i +1 i QDM constraints: Ground state: singlet No free nodes Each spin-1/2 belongs to No corner-sharing dimers one and only one VBS Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 3 / 43

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

Introduction to Quantum Dimer Model (QDM) Quantum dimer model Spin model Dimer d.o.f. are associated with the Spin d.o.f. are located in bonds of original lattice the nodes of the lattice � H = J 1 S i · S i +1 i Ground state: singlet QDM constraints: Each spin-1/2 belongs to No free nodes one and only one VBS No corner-sharing dimers Number of particles: 2 N r Number of particles: 3 N r − 2 Hilbert space: 2 2 N r Hilbert space: F ( N r ) Natalia Chepiga (SNF&UvA) Constrained models in 1D 31 July 2019 4 / 43

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