Infinite Matrix Product States for long range SU(N) spin models

Abstract

We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models.

arXiv comment37 pages, 6 figures

References in corpus (24)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• W-symmetry in Conformal Field Theory
• Criticality, the area law, and the computational power of PEPS
• Yang-Baxter equation in spin chains with long range interactions
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Explicit tensor network representation for the ground states of string-net models
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projected entangled-pair states can describe chiral topological states
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models
• The Sigma Model on Complex Projective Superspaces
• Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
• Quantisation of the SU(N) WZW Model at Level $k$
• Exact Dynamics of the SU(K) Haldane-Shastry Model
• Universality classes of dense polymers and conformal sigma models

Cited by in corpus (27)

• Full counting statistics in the Haldane-Shastry chain
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Matrix Product State description of the Halperin States
• Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
• Excited States in Spin Chains from Conformal Blocks
• Integrable open spin chains related to infinite matrix product states
• Lattice Laughlin states on the torus from conformal field theory
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• SU(3) trimer resonating-valence-bond state on the square lattice
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Many-body Lattice Wavefunctions From Conformal Blocks
• The BCS wave function, matrix product states, and the Ising conformal field theory
• A novel class of translationally invariant spin chains with long-range interactions
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients