2,022 research outputs found
Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models
A novel algorithm based on the optimized decimation of tensor networks with
super-orthogonalization (ODTNS) that can be applied to simulate efficiently and
accurately not only the thermodynamic but also the ground state properties of
two-dimensional (2D) quantum lattice models is proposed. By transforming the 2D
quantum model into a three-dimensional (3D) closed tensor network (TN)
comprised of the tensor product density operator and a 3D brick-wall TN, the
free energy of the system can be calculated with the imaginary time evolution,
in which the network Tucker decomposition is suggested for the first time to
obtain the optimal lower-dimensional approximation on the bond space by
transforming the TN into a super-orthogonal form. The efficiency and accuracy
of this algorithm are testified, which are fairly comparable with the quantum
Monte Carlo calculations. Besides, the present ODTNS scheme can also be
applicable to the 2D frustrated quantum spin models with nice efficiency
Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagom\'{e} lattice
The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied
by means of exact solutions and the tensor renormalisation group (TRG) method.
The zero-field phase diagrams are obtained, where three phases such as
ferromagnetic, ferrimagnetic and paramagnetic phases, along with the
second-order phase transitions, have been identified. The TRG results are quite
accurate and reliable in comparison to the exact solutions. In a magnetic
field, the magnetization (), susceptibility and specific heat are studied by
the TRG algorithm, where the plateaux are observed in the magnetization
curves for some couplings. The experimental data of susceptibility for the
complex Co(N)(bpg) DMF are fitted with the TRG results,
giving the couplings of the complex and
Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
We explore the frustrated spin- Heisenberg model on the star lattice
with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic
(FM) inter-triangle couplings (), and calculate its magnetic and
thermodynamic properties. We show that the FM couplings do not sabotage the
magnetic disordering of the ground state due to the frustration from the AF
interactions inside each triangle, but trigger a fully gapped
inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with
emergent spin-1 degrees of freedom. We discover that with strengthening ,
the system scales exponentially, either with or without a magnetic field :
the order parameter, the five critical fields that separate the -
ground-state phase diagram into six phases, and the excitation gap obtained by
low-temperature specific heat, all depend exponentially on . We calculate
the temperature dependence of the specific heat, which can be directly compared
with future experiments.Comment: 7 pages, 6 figure
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