Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model

Abstract

We show that infinite Matrix Product States (MPS) constructed from conformal field theories can describe ground states of one-dimensional critical systems with open boundary conditions. To illustrate this, we consider a simple infinite MPS for a spin-1/2 chain and derive an inhomogeneous open Haldane-Shastry model. For the spin-1/2 open Haldane-Shastry model, we derive an exact expression for the two-point spin correlation function. We also provide an SU($n$) generalization of the open Haldane-Shastry model and determine its twisted Yangian generators responsible for the highly degenerate multiplets in the energy spectrum.

5+7 pages, 4 figures, published version, a typo in the twisted Yangian generators corrected (thanks to the authors of arXiv:1511.08613 for pointing out this typo)

References in corpus (7)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix product states represent ground states faithfully
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Infinite Matrix Product States for long range SU(N) spin models
• Excited States in Spin Chains from Conformal Blocks
• Construction of spin models displaying quantum criticality from quantum field theory

Cited by in corpus (16)

• Full counting statistics in the Haldane-Shastry chain
• Integrable open spin chains related to infinite matrix product states
• 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
• Many-body Lattice Wavefunctions From Conformal Blocks
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• The BCS wave function, matrix product states, and the Ising conformal field theory
• The open Haldane-Shastry chain: thermodynamics and criticality
• A novel class of translationally invariant spin chains with long-range interactions
• Exactly solvable quantum impurity model with inverse-square interactions
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Chain and ladder models with two-body interactions and analytical ground states
• Quantum impurity models from conformal field theory
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid