A New Numerical Approach Toward MPS State on Spin Ladder Systems

J. Piekarewicz, James R. Shepard

Zong-Zhen Pan, Shi-Jie Yang, Yi Zheng

Abstract We investigate the Mott insulating phases of a two-component bosonic lattice gas in the presence of gauge field. Such a system is described by a two-leg ladder model with an unconventional flux. The synthetic flux is generated by the spin-dependent tunneling and the site-dependent spin-flip. In the Mott regime, these two effects lead to Dzyaloshinskii-Moriya (DM) interaction and an external field that is rotating in the xy-plane. We obtain a very general XYZ model with the DM interaction, the spiral field, and the transverse field. Various interesting magnetic Hamiltonians can be covered by adjusting lattice parameters. The DM interaction or the spiral field can lead to spiral order when they appear alone. The interplay of DM coupling and spiral field leads to the emergence of a new multi-frequency spiral order between the paramagnetic phase and the spiral ferromagnetic phase. Ground state phases are investigated by focusing on order parameters, spin-spin correlation functions, and structure factors. Calculations are performed by using time evolution block decimation (TEBD) based on matrix product state (MPS).

Shohei Abe, Tôru Sakai, Kiyomi Okamoto +1 more

The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.

Jonas Richter, Fengping Jin, Lars Knipschild +5 more

Zhendong Li, Garnet Kin‐Lic Chan

We present a new wavefunction ansatz that combines the technique of spin projection with the language of matrix product states (MPS) and matrix product operators (MPO) as used in the density matrix renormalization group (DMRG). Specifically, spin-projected matrix product states (SP-MPS) are constructed as |Ψ^(N,S,M)_SP−MPS⟩=P_S|Ψ(N,M)_MPS⟩, where P_S is the spin projector for total spin S and |Ψ(N,M)MPS⟩ is an MPS wavefunction with a given particle number N and spin projection M. This new ansatz possesses several attractive features: (1) It provides a much simpler route to achieve spin-adaptation (i.e. to create eigenfunctions of Ŝ^2) compared to explicitly incorporating the non-Abelian SU(2) symmetry into the MPS. In particular, since the underlying state |Ψ(N,M)MPS⟩ in the SP-MPS uses only Abelian symmetries, one does not need the singlet embedding scheme for non-singlet states, as normally employed in spin-adapted DMRG, to achieve a single consistent variationally optimized state. (2) SP-MPS are closely connected to broken symmetry mean-field states. This allows to straightforwardly generate the large number of broken symmetry guesses needed to explore complex electronic landscapes in magnetic systems. Further, this connection can be exploited in the future development of quantum embedding theories for open-shell systems. (3) The sum of MPOs representation for the Hamiltonian and spin projector P_S naturally leads to an embarrassingly parallel algorithm for computing expectation values and optimizing SP-MPS. (4) Optimizing SP-MPS belongs to the variation-after-projection (VAP) class of spin projected theories. Unlike usual spin projected theories based on determinants, the SP-MPS ansatz can be made essentially exact simply by increasing the bond dimensions in |Ψ(N,M)MPS⟩. Computing excited states is also simple by imposing orthogonality constraints, which are simple to implement with MPS. To illustrate the versatility of SP-MPS, we formulate algorithms for the optimization of ground and excited states, develop perturbation theory based on SP-MPS, and describe how to evaluate spin-independent and spin-dependent properties such as the reduced density matrices. We demonstrate the numerical performance of SP-MPS with applications to several models typical of strong correlation, including the Hubbard model, and [2Fe-2S] and [4Fe-4S] model complexes.

S. J. Gibson