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 systems in two dimensions

1990 ◽  
Vol 68 (12) ◽  
pp. 1410-1418 ◽  
Author(s):  
D. D. Betts ◽  
S. Miyashita
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Magnetic Phase ◽  
Finite Lattice ◽  
Two Dimensions ◽  
Quantum Spin ◽  
Spin Systems ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
Quantum Spin Systems

We consider the zero-temperature properties of four different spin 1/2 models on two-dimensional lattices: the XY ferromagnet, the XY antiferromagnet, the Heisenberg antiferromagnet, and the Dzyaloshinsky–Moriya models. Most of this article is a review of previously published work, but a few previously unpublished results are included. The relation between three of the models on bipartite lattices is described. The properties of the XY ferromagnet in two dimensions, especially those derived from extrapolation of finite lattice results, are reviewed. A numerical factor by which spin-wave and finite-lattice estimates of the long-range order parameter differ is discussed. For frustrated models on the triangular lattice the possibility of a chirality phase transition instead of, or in addition to, a magnetic phase transition is considered.

The complexity of quantum spin systems on a two-dimensional square lattice

2008 ◽  
Vol 8 (10) ◽  
pp. 900-924
Author(s):  
R. Oliveira ◽  
B.M. Terhal
Keyword(s):  
Perturbation Method ◽  
Quantum Computation ◽  
Quantum Spin ◽  
Circuit Model ◽  
Spin Systems ◽  
Square Lattice ◽  
Two Dimensional ◽  
Quantum Spin Systems ◽  
Local Interactions ◽  
Side Result

The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.

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

Generalized Zero-Temperature Glauber Dynamics in a Two-Dimensional Square Lattice

2012 ◽  
Vol 29 (12) ◽  
pp. 120502
Author(s):  
Qing-Kuan Meng ◽  
Dong-Tai Feng ◽  
Xu-Tuan Gao ◽  
Yu-Xue Mei
Keyword(s):  
Glauber Dynamics ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Generalized Zero

Exact ground states of one- and two-dimensional frustrated quantum spin systems

2002 ◽  
pp. 769-810
Author(s):  
A.A. Ovchinnikov ◽  
V.Ya. Krivnov ◽  
D.V. Dmitriev
Keyword(s):  
Ground States ◽  
Quantum Spin ◽  
Spin Systems ◽  
Two Dimensional ◽  
Quantum Spin Systems

scholarly journals Large-q expansion of the two-dimensional q-state Potts model by the finite lattice method

1999 ◽  
Vol 73 (1-3) ◽  
pp. 754-756
Author(s):  
H. Arisue ◽  
K. Tabata
Keyword(s):  
Potts Model ◽  
Finite Lattice ◽  
Two Dimensional ◽  
Lattice Method

MONTE CARLO STUDY OF QUANTUM SPIN SYSTEMS ON THE SQUARE LATTICE

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1393-C8-1394 ◽  
Author(s):  
Y. Okabe ◽  
M. Kikuchi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Quantum Spin ◽  
Spin Systems ◽  
Square Lattice ◽  
Quantum Spin Systems
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