EXACT STEADY STATES OF ASYMMETRIC DIFFUSION AND TWO-SPECIES ANNIHILATION WITH BACK REACTION FROM THE GROUND STATE OF QUANTUM SPIN MODELS

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3449-3461 ◽  
Author(s):  
FRANCISCO C. ALCARAZ
Keyword(s):  
Ground State ◽  
Heisenberg Model ◽  
Quantum Spin ◽  
Back Reaction ◽  
Dynamical Models ◽  
Exact Probability ◽  
Exact Probability Distribution ◽  
Quantum Spins ◽  
Quantum Spin Models ◽  
The Relationship

We calculated the exact probability distribution of the equilibrium state of some dynamical models in d-dimensional hypercubic lattices (d≥1). In these models we have asymmetric diffusion or two-species annihilation with back reaction A+B↔Ø. Our results are derived by exploring the relationship between the master equation and the Hamiltonian of quantum spins. The models we study are related to the spin-S Heisenberg model.

scholarly journals Ground-state properties of linear-exchange quantum spin models

2012 ◽  
Vol 100 (2) ◽  
pp. 27003 ◽  
Author(s):  
Bimla Danu ◽  
Brijesh Kumar ◽  
Ramesh V. Pai
Keyword(s):  
Ground State ◽  
Quantum Spin ◽  
Spin Models ◽  
Ground State Properties ◽  
Quantum Spin Models ◽  
Linear Exchange

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 Dimerization in Quantum Spin Chains with O(n) Symmetry

2021 ◽  
Author(s):  
Jakob E. Björnberg ◽  
Peter Mühlbacher ◽  
Bruno Nachtergaele ◽  
Daniel Ueltschi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Dimensional System ◽  
Quantum Spin Chains ◽  
One Dimensional ◽  
Open Region ◽  
Quantum Spins ◽  
The One

AbstractWe consider quantum spins with $$S\ge 1$$ S ≥ 1 , and two-body interactions with $$O(2S+1)$$ O ( 2 S + 1 ) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.

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.

scholarly journals AB INITIO CALCULATIONS FOR THE SQUARE-LATTICE ANISOTROPIC HEISENBERG MODEL

1999 ◽  
Vol 13 (05n06) ◽  
pp. 709-719
Author(s):  
R. F. BISHOP ◽  
D. J. J. FARNELL
Keyword(s):  
Ab Initio ◽  
Ground State ◽  
Heisenberg Model ◽  
Quantum Phase Transitions ◽  
Quantum Spin ◽  
Square Lattice ◽  
Cluster Method ◽  
Xy Model ◽  
Quantum Spin Systems ◽  
Anisotropic Heisenberg Model

Interest in lattice quantum spin systems as models of quantum magnets has increased with the discovery of new and interesting magnetic materials. Here we use a well-known technique of quantum many-body theory, namely the coupled-cluster method (CCM), to investigate the nearest-neighbour, spin-½, anisotropic Heisenberg model on the square lattice. Ground-state expectation values for quantities such as the ground-state energy and the sublattice magnetisation are determined to an accuracy comparable with that of the best of other available techniques including Monte Carlo methods. In order to demonstrate this point we present results for various values of the anisotropy parameter, including those for the isotropic Heisenberg model and the isotropic XY model. We show that it is now possible to determine the presence and position of the quantum phase transitions using ab initio CCM calculations, and furthermore that we can accurately predict the critical behaviour at these points.

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