Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice

Abstract

We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (ie self-conjugate $6$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimer-like phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauthé, S. Capponi and D. Poilblanc, Phys. Rev. B $\text{99}$, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric Projected Entangled Pair States (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations.

References in corpus (10)

• A one-dimensional liquid of fermions with tunable spin
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Exact Diagonalization of Heisenberg SU(N) models
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Dynamics at and near conformal quantum critical points
• SU(N) quantum spin models: A variational wavefunction study
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• SU(4) topological RVB spin liquid on the square lattice
• Entanglement properties of the two-dimensional SU(3) AKLT state

Cited by in corpus (11)

• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Superconducting stripes in the hole-doped three-band Hubbard model
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Efficient tensor network algorithm for layered systems
• Spectral functions with infinite projected entangled-pair states
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Exploiting the Hermitian symmetry in tensor network algorithms
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS
• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice