Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice

Abstract

In the physics of the Fractional Quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin-like systems, we propose a family of SU($N$)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for arbitrary $N$ of an SU($3$) model studied previously where time-reversal symmetry is broken explicitly. Guided by the recent discovery of SU($2$)${}_1$ and SU($3$)${}_1$ chiral spin liquids (CSL) on similar models we search for topological SU($N$)${}_1$ CSL in some range of the Hamiltonian parameters via a combination of complementary numerical methods such as exact diagonalizations (ED), infinite density matrix renormalization group (iDMRG) and infinite Projected Entangled Pair State (iPEPS). Extensive ED on small (periodic and open) clusters up to $N=10$ and an innovative SU($N$)-symmetric version of iDMRG to compute entanglement spectra on (infinitely-long) cylinders in all topological sectors provide unambiguous signatures of the SU($N$)${}_1$ character of the chiral liquids. An SU($4$)-symmetric chiral PEPS, constructed in a manner similar to its SU($2$) and SU($3$) analogs, is shown to give a good variational ansatz of the $N=4$ ground state, with chiral edge modes originating from the PEPS holographic bulk-edge correspondence. Finally, we discuss the possible observation of such Abelian CSL in ultracold atom setups where the possibility of varying $N$ provides a tuning parameter similar to the magnetic field in the physics of the FQH effect.

arXiv comment41 pages, 21 figures, references added, figure 2(j) modified, abstract and introduction revised

References in corpus (78)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Liquid States
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum Orders and Symmetric Spin Liquids
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Fractional Chern Insulator
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Corner Transfer Matrix Renormalization Group Method
• Applied Conformal Field Theory
• A one-dimensional liquid of fermions with tunable spin
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• An exact chiral spin liquid with non-Abelian anyons
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Entanglement spectrum and boundary theories with projected entangled-pair states
• PEPS as ground states: degeneracy and topology
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Characterizing topological order by studying the ground states of an infinite cylinder
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Resonating valence bond states in the PEPS formalism
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Infinite size density matrix renormalization group, revisited
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Fractional quantum Hall states in lattices: Local models and physical implementation
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Nature of chiral spin liquids on the kagome lattice
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Quantum critical phase with infinite projected entangled paired states
• Parent Hamiltonian for the Chiral Spin Liquid
• Exact Diagonalization of Heisenberg SU(N) models
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Chiral topological spin liquids with projected entangled pair states
• X-Symbols for Non-Abelian Symmetries in Tensor Networks
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Tensor network representations of parton wave functions
• Synthetic gauge fields stabilize a chiral spin liquid phase
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Infinite Matrix Product States for long range SU(N) spin models
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• A programming guide for tensor networks with global $SU(2)$ symmetry
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Density matrix renormalization group boosted by Gutzwiller projected wave functions
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy
• Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions
• Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
• Abelian and non-abelian symmetries in infinite projected entangled pair states
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice
• Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

Cited by in corpus (25)

• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Theory of competing Chern-Simons orders and emergent phase transitions
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Possible chiral spin liquid state in the $S=1/2$ kagome Heisenberg model
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Chiral spin liquid in a ${\mathbb{Z}}_3$ Kitaev model
• Efficient conversion from fermionic Gaussian states to matrix product states
• Simulating chiral spin liquids with projected entangled-pair states
• Classical and quantum spin liquids
• Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• 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
• Detuning the Floquet anomalous chiral spin liquid