https://wiki.symmps.eu/ 2026-05-06T11:02:54+0000 https://wiki.symmps.eu/ https://wiki.symmps.eu/lib/tpl/dokuwiki/images/favicon.ico text/html 2019-06-04T21:39:11+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:implementation&rev=1559684351&do=diff Implementation DMRG In this section the implementation of the relevant Java classes of the applet is explained. Though the applet just implements a spin-\(\frac{1}{2}\)-chain, all classes will have a variable number of local parameters. Matrix [Anordnung der Matrixelemente ((Author: HB, Lizenz: Creative Common by-sa, Source: http://commons.wikimedia.org/wiki/File:Matrice.svg?uselang=de))] The class “Matrix\(\hat W^{\left[i\right]}\)$\hat W^{\left[i\right]}$$\hat W^{\left[i\right]}$$H_{\text{… text/html 2011-10-13T07:46:30+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:links&rev=1318491990&do=diff Links Here you can find some links to other web pages containing information about MPS/DMRG: * Steven White's Homepage - the inventor of the DMRG * Tomotoshi Nishino DMRG page - Here you can also find a one-particle DMRG Applet (documentation in Japanese) * Eric Jeckelmann's DMRG text/html 2019-06-04T21:37:56+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:matrix_product_states&rev=1559684276&do=diff Matrix Product States Matrix Product States (mps) are an efficient approximation for a general weakly-entangled quantum state. The main idea is to approximate a general quantum state by a sum of simple product states. This sum of product states is generated by a matrix product of $d\cdot n$$n$$d$$L$$\sigma_i=\{\uparrow, \downarrow\}$\begin{align} \lvert\psi\rangle = \sum_{\sigma_1, \ldots, \sigma_L} c_{\sigma_1\ldots\sigma_L} \lvert {\sigma_1, \ldots, \sigma_L} \rangle \end{align}$(c_{\sigma_1\… text/html 2019-06-04T21:35:57+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:start&rev=1559684157&do=diff Welcome to the Matrix Product States - DMRG Applet - Wiki Here we give an introduction to Matrix Product States and the use of the DMRG-applet. The wiki is based on the (german) bachelor thesis of Thomas Köhler: [„Die Dichte-Matrix-Renormierungsgruppe für die tranversale Ising-Quanten-Kette: Ein Demonstrationsprogramm“]. The introduction to the Matrix Product States is mainly based on the review article text/html 2019-06-04T21:40:52+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:tests&rev=1559684452&do=diff Examples / test cases In this chapter we will present some examples for the applet and compare them with analytical solutions. You can easily reproduce the simulations just by clicking on the link and the applet will be started with these values. Ising-Model (without magnetic field) \(\hat H\)\begin{equation*} \hat H= J^z\sum_{i=1}^{N-1}\hat S_i^z \hat S_{i+1}^z \end{equation*}\begin{equation*} E_0 = -\frac{(N-1)\cdot \lvert J^z\lvert}{4} \end{equation*}\begin{equation*} E_0 = -\frac{(8-1)\cdo… text/html 2019-06-04T21:40:16+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:usage&rev=1559684416&do=diff Usage This chapter will introduce to the usage of the applet. Screenshots Here you see two screenshots of the applet: main window The main window consists of four plots. These give the value of the groundstate energy, the expectation values for \(S^x\)\(S^z\)\(S^+\)\(S^-\)\(S^x\)\(S^y\)\begin{equation*} H=\frac{J}{2} (S^+S^- + S^-S^+)+J^z S^zS^z+h^zS^z+h^xS^x \end{equation*}\begin{equation*} H=J^xS^xS^x + J^yS^yS^y+J^z S^zS^z+h^zS^z+h^xS^x \end{equation*} text/html 2011-10-10T13:36:32+0000 Anonymous (anonymous@undisclosed.example.com) https://wiki.symmps.eu/doku.php?id=en:variational_groundstate_search&rev=1318253792&do=diff Variational Groundstate Search Here we introduce the variational groundstate search for matrix product states. The goal is to find the MPS representation of the groundstate of the onedimensional lattice with a given hamiltonian H. Furthermore we limit the matrix dimension m of the matrices in the MPS to a maximal value. Therefore we try to find the best MPS representation of the groundstate for a given matrix dimension m.$\lvert\psi\rangle$\begin{align} E = min\frac{\langle\psi\lvert\hat H\lver…