2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009;
Pittsburgh, Pennsylvania
Session A8: Quantum Information meets Many-Particle Physics
8:00 AM–11:00 AM,
Monday, March 16, 2009
Room: 414/415
Sponsoring
Unit:
GQI
Chair: David DiVincenzo, IBM Watson
Abstract ID: BAPS.2009.MAR.A8.3
Abstract: A8.00003 : Tensor-entanglement renormalization
9:12 AM–9:48 AM
Preview Abstract
Abstract
Author:
Zhengcheng Gu
(M.I.T.)
Traditional mean-field theory is a simple generic variational approach for
analyzing various symmetry breaking phases. However, this simple approach
only applies to symmetry breaking states with short-range entanglement.
Tensor-entanglement renormalization group (TERG) is a generic approach for
studying 2D quantum phases with long-range entanglement (such as topological
phases) based on a new class of trial wavefucntions - the tensor product
states (TPS), also known as projected entangled pair states (PEPS). Those
TPS (PEPS) are built from local tensors. They can describe both states with
short-range entanglement (such as the symmetry breaking states) and states
with long-range entanglement (such as topological/quantum order).
TERG is a real space renormalization group algorithm that can efficiently
simulate expectation values for TPS wave functions in 2D and higher
dimensions. As an attempt in this direction, we demonstrate our algorithm by
studying several simple 2D quantum spin models, including both symmetry
breaking phase transitions and topological phase transitions.
However, as any variational method, the TERG approach could not find all the
degenerate ground states for gapped systems and generally could not give out
(approximately) correct critical exponent for critical systems. To solve
these problems, we study the renormalization group flow of a Lagrangian
(partition function) by representing its path integral through a tensor
network. Using a tensor-entanglement-filtering renormalization group (TEFRG)
method that removes local entanglement and coarse grains the lattice, we
show that the renormalization flow of the tensors in the tensor network has
a nice fixed-point structure. The isolated fixed-point tensors characterize
various phases. The tensor fixed points can describe both the symmetry
breaking phases and topological phases. The ground state degeneracy for
gapped systems can be easily read out from the fixed point tensor. The
scaling dimensions, the central charge and dynamic correlation functions for
the critical systems that describe the continuous phase transitions between
symmetry breaking and/or topological phases can also be calculated from the
TEFRG approach.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.A8.3