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

1987 ◽  
Vol 65 (1) ◽  
pp. 76-81 ◽  
Author(s):  
S. Fujiki ◽  
D. D. Betts
Keyword(s):  
Triangular Lattice ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Transverse Spin ◽  
Nearest Neighbour ◽  
Spin Correlations ◽  
Infinite Lattice ◽  
Longitudinal Correlation ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] antiferromagnet has been extended to an N = 21 site triangular lattice. By fitting a quadratic in 1/N to the nearest neighbour transverse spin correlations, we have estimated the ground-state energy per bond on the infinite lattice to be E0/3NJ = −0.2716 ± 0.005. The nearest neighbour longitudinal correlation is estimated to be [Formula: see text]. A short-range order parameter, the chirality, is defined and estimated for the infinite lattice. From the N dependence of the three sublattice or helical magnetization, the spin correlation is conjectured to decay algebraically as [Formula: see text].

Zero-temperature properties of quantum spin models on a triangular lattice I: the ferromagnet

1986 ◽  
Vol 64 (8) ◽  
pp. 876-881 ◽  
Author(s):  
S. Fujiki ◽  
D. D. Betts
Keyword(s):  
Triangular Lattice ◽  
Ground State ◽  
State Energy ◽  
Quantum Spin ◽  
Nearest Neighbour ◽  
Zero Temperature ◽  
Pair Correlations ◽  
Spin Correlations ◽  
Longitudinal Correlation ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] ferromagnet has been extended to an N = 21 site triangular lattice. By fitting a quadratic in 1/N to the nearest neighbour transverse pair correlations, we have estimated the ground-state energy per bond on the infinite lattice to be E0/3NJ = −0.5326 ± 0.003. We conjecture that the square of the magnetization per site vanishes very sharply as N−0.06. The nearest neighbour longitudinal correlation per bond [Formula: see text] for all two-dimensional lattices.

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 Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Christian Wessler ◽  
Bertrand Roessli ◽  
Karl W. Krämer ◽  
Bernard Delley ◽  
Oliver Waldmann ◽  
...  
Keyword(s):  
Quantum Critical Point ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Honeycomb Lattice ◽  
Spin Liquids ◽  
Spin Correlations ◽  
Quantum Spin Liquids ◽  
Dynamic Spin ◽  
New Perspective ◽  
The Continuum

AbstractQuantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3 avoids order down to at least T = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.

Exact diagonalization of the S = 1/2 XY ferromagnet on a new set of finite triangular lattices at T = 0

2003 ◽  
Vol 81 (3) ◽  
pp. 555-571
Author(s):  
D D Betts ◽  
K S Lee ◽  
H Q Lin
Keyword(s):  
Triangular Lattice ◽  
Exact Diagonalization ◽  
Spin Correlations ◽  
The Past ◽  
Infinite Lattice ◽  
Finite Lattices ◽  
Triangular Lattices ◽  
Scalar Equations

We have obtained 85 finite triangular lattices from 7 to 36 vertices. We display two very good finite lattices – 21a (well-known) and 22a (previously unknown). Over the past decade several physicists have used exact diagonalization on five tripartite triangular lattices from N = 9 to 36 to study the Heisenberg and XY antiferromagnet on the infinite triangular lattice. Nine more tripartite triangular lattices are available as shown below in the text. Our exact diagonalization of the S = 1/2 XY ferromagnetic energies and magnetization leads, by scalar equations, to the properties on the infinite lattice. We found that all but 10 of the 85 are good lattices. Finally, we obtained spin–spin correlations of two kinds, xx and zz. PACS Nos.: 75.10Jm, 05.05+q

scholarly journals Site-Monotonicity Properties for Reflection Positive Measures with Applications to Quantum Spin Systems

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Benjamin Lees ◽  
Lorenzo Taggi
Keyword(s):  
Spin Correlation ◽  
Quantum Spin ◽  
Heisenberg Antiferromagnet ◽  
Quantum Spin Systems ◽  
Point Function ◽  
Dimer Model ◽  
Spin Correlations ◽  
Mechanics Model ◽  
Monotonicity Properties ◽  
General Statistical

AbstractWe consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model and lattice permutations, thus extending the previous results of Lees and Taggi (2019).

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 A Modified Quantum Renormalization Group for XXZ Spin Chain

1998 ◽  
Vol 12 (23) ◽  
pp. 2359-2370
Author(s):  
A. Langari ◽  
V. Karimipour
Keyword(s):  
Renormalization Group ◽  
Ground State ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Spin Systems ◽  
Heisenberg Chain ◽  
Quantum Spin Systems ◽  
Xxz Model ◽  
Simple Modification

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the XXZ spin-[Formula: see text] Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin–spin correlation function which confirms the absence of long-range order in the massless region of the 1D XXZ model.

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