ALPSを使った...

ALPSを使ったスピン格子系の数値シミュレーション

2014. 02. 27.小野俊雄

114年2月27日木曜日

What is ALPS?

• 実験家の利点：相互作用パラメータの決定

• 的外れなモデルを立てていないか？をチェックできる!

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ALPSチュートリアル – ALPSの概要ALPSプロジェクト

ALPSとは?

ALPS = Algorithms and Libraries for Physics Simulations

量子スピン系, 電子系など強相関量子格子模型のシミュレーションためのオープンソースソフトウェアの開発を目指す国際共同プロジェクトALPSライブラリ = C++による格子模型のための汎用ライブラリ群ALPSアプリケーション = 最新のアルゴリズムに基づくアプリケーション群: QMC, DMRG, ED, DMFT等ALPSフレームワーク = 汎用入出力形式, 解析ツール, スケジューラなど, 大規模並列シミュレーションのための環境

9 / 27


Setup step1: download binary files• You need to download 3 packages

1. alps-2.2.b1-winXX.exe (XX = 32 or 64)• 数値計算ライブラリ本体

2. alps-vistrails-2.2.b1-winXX.exe• PythonからALPSを動かす拡張コマンド

3. vistrails-setup-2.1.1-90975fc00211.zip• Pythonの環境：データの抽出・グラフ描画・ファイル書き出し

(Version numbers are those as of Feb. 2014.)


Setup step1: download binary files

Setup and Installation

Web page: http://alps.comp-phys.org/



バイナリパッケージ



32 bit or 64 bit?



32 bit

64 bit

Caution! Release 2.1.1 (stable version) seems to do NOT work on Windows 7.


Setup step1: download binary filesWeb page: http://ww.vistrails.org/

Downloading VisTrails



32 bit

64 bit


Setup step2: Install Packages1. Install alps-2.2.b1

Choose one of these two

1-1. Start installer

1-2. Choose“Add alps to the system PATH for ...”


Setup step2: Install Packages2. Install VisTrails 2.1.1

Unzip by right-clicking

2-2. Open the installer and install package.

2-1. Unzip downloaded file.

Python tools for ALPScollecting the data from the resultsexporting the .txt filesmaking plots of the results


Setup step2: Install Packages3. Install alps-vistrails-2.2.b1

Execute the installer

ソフトのインストールはここまで

ALPS extensions for VisTrails


Setup step3: Configure & Test

初期設定

1. Start VisTrails.

2. Select “Preference...” in Edit menu.

1. Start VisTrails & Open preference panel.



• Select “Module Packages” tab.

• Enable ‘matplotlib’, ‘vtlcreator’ and ‘alps’ modules in this order.

2. Enable several python modules in the panel

①

②

③

セットアップの完了1414年2月27日木曜日


• You can find many tutorial files in C:\Program Files\ALPS\tutorials\

• tutorial3b.py: magnetization process of the S=1/2 spin ladder system

3. First run of the quantum Monte Carlo simulation



• Create a new folder and put a copy of the tutorial file in that folder.

• Type “vispython tutorial3b.py” at the command prompt.

3. First run of the quantum Monte Carlo simulation

created folder

copied file

command to launch Python


Demo


Workflow of the simulation 1. Define the spin network• Cluster (Molecular magnets such as V15)• Lattice• preinstalled: dimer, 1D chain, square (rectangular)

lattice, (coupled) ladder, triangular lattice, kagome lattice, honeycomb lattice

2. Set parameters for the simulation(s)• Magnitude of the exchange interaction(s)• Temperature & Magnetic field• Algorithm of Monte Carlo simulation

(looper, dirloop SSE....)• Physical quantity• Output data (text files, data visualization)

3. Start simulation1914年2月27日木曜日

Basic procedures of the simulation

Python scriptwith

parameters

my_simulation.py

Lattice XML file Model XML file

definitions of operators

Output files

Plots, Text files

square lattice

Definition ofthe lattice

Parameters of the simulation


Structure of ‘Lattice.xml’ file

<LATTICE name=”lattice name”>格子（unit cellの並べ方）の定義

</LATTICE>

<UNITCELL name=”unitcell name”>ユニットセルの内部構造

</UNITCELL>

<LATTICEGRAPH name=”spin network”><FINITELATTICE>

<LATTICE ref=”lattice name”/><EXTENT size=”L”/><BOUNDARY type=”periodic”/>

</FINITELATTICE><UNITCELL ref=”unitcell name”/>

</LATTICEGRAPH>

格子の参照サイズの指定境界条件

unitcellの参照

有限格子の名前この名前が参照される

<LATTICES>

</LATTICES>2114年2月27日木曜日

Example 1: alternating chain

• 方針：1次元的に並ぶunit cellに，　　　2つのsiteと2つのbondを持つ‘内部構造’を与える

1

offset=0 offset=1

2 1 2

offset=2 offset=3

1 2 1 2

<LATTICE name="chain lattice" dimension="1"> <PARAMETER name="a" default="1"/> <BASIS><VECTOR>a</VECTOR></BASIS> <RECIPROCALBASIS><VECTOR>2*pi/a</VECTOR></RECIPROCALBASIS></LATTICE>

<LATTICE name=”lattice name”>格子（unit cellの並べ方）の定義

</LATTICE>

C:\Program Files\ALPS\lib\xml\lattice.xml のchain latticeの定義を利用する2214年2月27日木曜日


• サイト　→　VERTEX, ボンド　→　EDGE

1

offset=0 offset=1

2 1 2

offset=2 offset=3

1 2 1 2

<UNITCELL name=”unitcell name”>ユニットセルの内部構造

</UNITCELL>

<UNITCELL name="alt chain unit" dimension="1" vertices="2"> <VERTEX id="1"><COORDINATE> 0.00 </COORDINATE></VERTEX> <VERTEX id="2"><COORDINATE> 0.50 </COORDINATE></VERTEX> <EDGE type="0"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="1" offset="1"/></EDGE></UNITCELL>

corresponds to J0corresponds to J1

J1J0



• 3つのブロックの組み合わせ

<LATTICE name="chain lattice" dimension="1"> <PARAMETER name="a" default="1"/> <BASIS><VECTOR>a</VECTOR></BASIS> <RECIPROCALBASIS><VECTOR>2*pi/a</VECTOR></RECIPROCALBASIS></LATTICE>

<UNITCELL name="alt chain unit" dimension="1" vertices="2"> <VERTEX id="1"><COORDINATE> 0.00 </COORDINATE></VERTEX> <VERTEX id="2"><COORDINATE> 0.50 </COORDINATE></VERTEX> <EDGE type="0"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="1" offset="1"/></EDGE></UNITCELL>

<LATTICEGRAPH name="alt chain"> <FINITELATTICE> <LATTICE ref="chain lattice"/> <PARAMETER name="L"/> <EXTENT dimension="1" size="L"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL ref="alt chain unit"/></LATTICEGRAPH>

<LATTICES>

</LATTICES>

altchain_def.xml


格子の定義ファイル2414年2月27日木曜日

Example 1: alternating chain• Python script for the simulation of the magnetization process

parms = []for h in [0.0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3]: parms.append( { 'LATTICE' : "alt chain", 'LATTICE_LIBRARY' : "altchain_def.xml", 'MODEL' : "spin", 'local_S' : 0.5, 'T' : 0.02, 'J0' : 1.0 , 'J1' : 0.30 , 'THERMALIZATION' : 1000, 'SWEEPS' : 10000, 'L' : 40, 'h' : h } )

import pyalpsimport matplotlib.pyplot as pltimport pyalps.plot

Import necessary modules

Set parameters for the mh-curve simulation

name of ‘LATTICE GRAPH’

name of definition file

magnetic fields

magnitude of interactions


print "The results in plain text are:"print pyalps.plot.convertToText(magnetization)print "Saving int file alt_mh.txt"f = open ('alt_mh.txt','w')f.write(pyalps.plot.convertToText(magnetization))f.close()

input_file = pyalps.writeInputFiles('parm_altchain',parms)res = pyalps.runApplication('dirloop_sse',input_file,Tmin=5)

data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm_altchain'),'Magnetization Density')magnetization = pyalps.collectXY(data,x='h',y='Magnetization Density')

Create input_file for Monte Carlo program & start simulation

Collect desired physical quantity & create data array of M vs. H

Print result & write into a text file for



• You can adjust the temperature used in the experiments.

0.5

0.4

0.3

0.2

0.1

0.0

Sz

2.52.01.51.00.50.0

gµBH / J

α = 0.30 α = 0.35 α = 0.40 α = 0.45 α = 0.50 α = 0.55 α = 0.60 α = 0.65 α = 0.70 α = 0.75 α = 0.80 α = 0.85 α = 0.90 α = 0.95 α = 1.00

kBT = 0.02 J


Example: tricolor bond honeycombYasu Shinpuku


Mapping on an orthorhombic lattice

1 21 2 1 2

1 21 2 1 2

1 21 2 1 2

(0,0) (1,0)(-1,0)

(0,-1) (1,-1)(-1,-1)

(0,1) (1,1)(-1,1)


Description of the lattice

• Lattice: orthorhombic or square(arrangement of the unit cell)

• Unit Cell: 2 sites and 3bonds

• Lattice Graph: L x W

1 21 2 1 2

1 21 2 1 2

1 21 2 1 2

(0,0) (1,0)(-1,0)

(0,-1) (1,-1)(-1,-1)

(0,1) (1,1)(-1,1)


Inside of the definition file<LATTICE name="square lattice" dimension="2"> <PARAMETER name="a" default="1"/> <BASIS><VECTOR>a 0</VECTOR><VECTOR>0 a</VECTOR></BASIS> <RECIPROCALBASIS><VECTOR>2*pi/a 0</VECTOR><VECTOR>0 2*pi/a</VECTOR></RECIPROCALBASIS></LATTICE>

<UNITCELL name="honeycomb 3bonds unit" dimension="2"> <VERTEX id="1" type="1"><COORDINATE>0.25 0.5</COORDINATE></VERTEX> <VERTEX id="2" type="1"><COORDINATE>0.75 0.5</COORDINATE></VERTEX> <EDGE type="0"><SOURCE vertex="1"/><TARGET vertex="2/></EDGE> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="1" offset="1 0"/></EDGE> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2" offset="0 1"/></EDGE></UNITCELL>

<LATTICEGRAPH name = "honeycomb 3bonds lattice"> <FINITELATTICE> <LATTICE ref="square lattice"/> <PARAMETER name="W" default="L"/> <EXTENT dimension="1" size="L"/> <EXTENT dimension="2" size="W"/> <BOUNDARY type="open"/> </FINITELATTICE> <UNITCELL ref="honeycomb 3bonds unit"/></LATTICEGRAPH>

<LATTICES>

</LATTICES>

copied from ‘lattices.xml’

1 21 2 1 2

1 21 2 1 2

1 21 2 1 2

(0,0) (1,0)(-1,0)

(0,-1) (1,-1)(-1,-1)

(0,1) (1,1)(-1,1)


Calculated results1.0

0.8

0.6

0.4

0.2

0.0

M [µ

B / s

pin]

3.02.01.00.0B [T]

J1 / kB = -11.6 KJ2 / kB = 0.418 KJ3 / kB = 2.51 K

0.16

0.12

0.08

0.04

0.00

χ [ e

mu/

mol

]

0.1 1 10 100T [K]

J1 / kB = -11.6 KJ2 / kB = 0.418 KJ3 / kB = 2.51 K

0.5

0.4

0.3

0.2

0.1

0.0

χT [

emu

K / m

ol]

0.1 1 10 100T [K]

J1 / kB = -11.6 KJ2 / kB = 0.418 KJ3 / kB = 2.51 K


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