Improved finite-lattice estimates of the properties of two quantum spin models on the infinite square lattice

1999 ◽  
Vol 77 (5) ◽  
pp. 353-369 ◽  
Author(s):  
D D Betts ◽  
H Q Lin ◽  
J S Flynn
Keyword(s):  
Spin Wave ◽  
Quantum Monte Carlo ◽  
Finite Lattice ◽  
Exact Diagonalization ◽  
Quantum Spin ◽  
Square Lattice ◽  
Zero Temperature ◽  
Spin Models ◽  
And Topology ◽  
Quantum Spin Models

This paper describes an improvement in the method of exact diagonalization of Hamiltonians of quantum spin models on finite square lattices and the statistical analysis of the data so obtained to estimate the physical properties of the models on the infinite square lattices at zero temperature. The geometry and topology of finite square lattices are described. The models studied are the spin one-half XY and Heisenberg antiferromagnets using 28 finite square lattices with up to 32 vertices. Our estimates of the energy and magnetization on each model on the infinite lattice at zero temperature compare very well with recent estimates using quantum Monte Carlo, series expansion, and spin wave estimates. Estimates of spin wave velocity and transverse susceptibilities are more scattered.PACS No.: 75.10J

MODIFIED SPIN-WAVE THEORY FOR THE FRUSTRATED HEISENBERG ANTIFERROMAGNET ON A SQUARE LATTICE

2013 ◽  
Vol 27 (11) ◽  
pp. 1350021 ◽  
Author(s):  
YOU WU ◽  
YUAN CHEN
Keyword(s):  
Spin Wave ◽  
Quantum Monte Carlo ◽  
Present Method ◽  
Nearest Neighbors ◽  
Wave Theory ◽  
Exact Diagonalization ◽  
Quantum Spin ◽  
Square Lattice ◽  
Heisenberg Antiferromagnet ◽  
Spin Wave Theory

The effects of quantum fluctuations due to frustration between nearest neighbors and next-nearest neighbors of the quantum spin-half Heisenberg antiferromagnet on a square lattice are investigated by using the modified spin-wave theory (MSW). We have extended Takahashi's MSW theory, and studied the ground-state and finite-temperature properties of this model. The results calculated within this formalism on the thermodynamics agree quite well with the quantum Monte Carlo estimates, and exact diagonalization results. We have also compared the present method with the conventional spin wave theory.

COUPLED CLUSTER TREATMENTS OF QUANTUM MAGNETS: TWO EXAMPLES

2003 ◽  
Vol 17 (28) ◽  
pp. 5347-5365 ◽  
Author(s):  
SVEN E. KRÜGER ◽  
DAMIAN J. J. FARNELL ◽  
JOHANNES RICHTER
Keyword(s):  
Ground State ◽  
Quantum Monte Carlo ◽  
Quantum Spin ◽  
Square Lattice ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Temperature Phase ◽  
Nearest Neighbour ◽  
Zero Temperature ◽  
Quantum Spin Models

In this article we study the ground-state properties of two square-lattice Heisenberg quantum spin models with competing bonds using a high-order coupled cluster treatment. The first model is a spin-half model with competing nearest-neighbour bonds with and without frustration. We discuss the influence of quantum fluctuations on the ground-state phase diagram and in particular on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. The second model is a highly frustrated ferrimagnet, which contains one sublattice (A) entirely populated with spin-one spins and an other sublattice (B) entirely populated with spin-half spins. Sublattice A sites are nearest-neighbours to sublattice B sites and vice versa and frustration is introduced by next-nearest-neighbour bonds. The model shows two collinear ordered phases and a noncollinear phase in which (classically) the spin-one spins are allowed to cant at an angle. Both examples show that the coupled-cluster method is able to describe the zero-temperature transitions well and provides a consistent description of collinear, noncollinear, and disordered phases, for cases in which other standard techniques (e.g. the quantum Monte Carlo technique for spin systems which are frustrated) are not applicable.

Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

1996 ◽  
Vol 74 (1-2) ◽  
pp. 54-64 ◽  
Author(s):  
D. D. Betts ◽  
S. Masui ◽  
N. Vats ◽  
G. E. Stewart
Keyword(s):  
Spontaneous Magnetization ◽  
Finite Lattice ◽  
Quantum Spin ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Quantum Spin Systems ◽  
Lattice Method ◽  
Dimensional Lattice ◽  
Finite Lattices

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

Zero-temperature properties of quantum spin models on the triangular lattice III: the Heisenberg antiferromagnet

1987 ◽  
Vol 65 (5) ◽  
pp. 489-491 ◽  
Author(s):  
S. Fujiki
Keyword(s):  
Triangular Lattice ◽  
Ground State ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
Spin Models ◽  
Spin Correlations ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] Heisenberg antiferromagnet has been extended to an N = 21 site triangular lattice. The infinite-lattice ground state energy per bond is estimated to be E0/3NJ = −0.3678 ± 0.005 by fitting a quadratic in 1/N to the finite N data. The plaquette chirality order is slightly greater than in the XY antiferromagnet. The two-spin correlation is conjectured to decay as [Formula: see text].

scholarly journals Thermal tensor renormalization group simulations of square-lattice quantum spin models

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Han Li ◽  
Bin-Bin Chen ◽  
Ziyu Chen ◽  
Jan von Delft ◽  
Andreas Weichselbaum ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Quantum Spin ◽  
Square Lattice ◽  
Spin Models ◽  
Lattice Quantum ◽  
Quantum Spin Models

scholarly journals Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study

2012 ◽  
Vol 14 (11) ◽  
pp. 113006 ◽  
Author(s):  
Michał Maik ◽  
Philipp Hauke ◽  
Omjyoti Dutta ◽  
Jakub Zakrzewski ◽  
Maciej Lewenstein
Keyword(s):  
Monte Carlo ◽  
Long Range ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Quantum Spin ◽  
Spin Models ◽  
Long Range Interactions ◽  
Quantum Spin Models
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