One-dimensional projection of two-dimensional systems using spiral boundary conditions

Abstract

We introduce spiral boundary conditions (SBCs) as a useful tool for handling the shape of finite-size periodic clusters. Using SBCs, a lattice model for more than two dimensions can be exactly projected onto a one-dimensional (1D) periodic chain with translational invariance. Hence, the existing 1D techniques such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., can be effectively applied to the projected 1D model. First, we describe the 1D projection scheme for the two-dimensional (2D) square- and honeycomb-lattice tight-binding models in real and momentum space. Next, we discuss how the density of states and the ground-state energy approach their thermodynamic limits. Finally, to demonstrate the utility of SBCs in DMRG simulations, we estimate the magnitude of staggered magnetization of the 2D XXZ Heisenberg model as a function of XXZ anisotropy.

5 pages, 4 figures, supplementary material

References in corpus (6)

• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Deconfinement criticality for the spatially anisotropic triangular antiferromagnet with the ring exchange
• Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions
• Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem

Cited by in corpus (5)

• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
• Phase diagram of the Kitaev-Heisenberg model using various finite-size clusters
• 2D excitation information by MPS method on infinite helixes
• Nontrivial three-sublattice magnetization in the easy-axis spin-1/2 XXZ antiferromagnet on the triangular lattice