Stable Optimization of a Tensor Product Variational State

نویسندگان

  • Andrej Gendiar
  • Nobuya Maeshima
  • Tomotoshi Nishino
چکیده

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. The numerical stability and efficiency of the new method are examined through its application to the 3D Ising model.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stable Optimization of Tensor Product Variational State

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. Numerical stability and efficiency of the new method is examined through its ap...

متن کامل

Stable Optimization of Tensor Product Variational Functions

We consider a variational problem for three-dimensional (3D) classical lattice models, where the trial state is given by a uniform 2D product of local factors. Maximization of the variational partition function draws a self-consistent equation for the local factor. We propose a stable algorithm to solve the equation numerically when the variational function contains many degrees of freedom. Num...

متن کامل

The Z-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory

In this paper, using variational analysis and optimization techniques, we examine some fundamental analytic properties of Z-eigenvalues of a real symmetric tensor with even order. We first establish that the maximum Z-eigenvalue function is a continuous and convex function on the symmetric tensor space, and so, provide formulas of the convex conjugate function and ε-subdifferential of the maxim...

متن کامل

Tensor Product Variational Formulation for Quantum Systems

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group m...

متن کامل

Tensor product representation of a topological ordered phase: Necessary symmetry conditions

Citation Chen, Xie et al. " Tensor product representation of a topological ordered phase: Necessary symmetry conditions. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story mat...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008