Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions

被引：441

作者：

Jordan, J. ^{[1
]}

Orus, R. ^{[1
]}

Vidal, G. ^{[1
]}

Verstraete, F. ^{[2
]}

Cirac, J. I. ^{[3
]}

机构：

[1] Univ Queensland, Sch Phys Sci, Brisbane, Qld 4072, Australia

[2] Univ Vienna, Fak Phys, A-1090 Vienna, Austria

[3] Max Planck Inst Quanten Opt, D-85748 Garching, Germany

来源：

PHYSICAL REVIEW LETTERS | 2008年 / 101卷 / 25期

基金：

澳大利亚研究理事会;

关键词：

D O I：

10.1103/PhysRevLett.101.250602

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv: cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

引用

页数：4

共 21 条

[1] Entanglement renormalization and topological order [J].

Aguado, Miguel ;

Vidal, Guifre .

PHYSICAL REVIEW LETTERS, 2008, 100 (07)

[2] Cluster Monte Carlo simulation of the transverse Ising model -: art. no. 066110 [J].

Blöte, HWJ ;

Deng, YJ .

PHYSICAL REVIEW E, 2002, 66 (06) :8

[3] GROUND-STATE OF THE ELECTRON-GAS BY A STOCHASTIC METHOD [J].

CEPERLEY, DM ;

ALDER, BJ .

PHYSICAL REVIEW LETTERS, 1980, 45 (07) :566-569

[4] FINITELY CORRELATED STATES ON QUANTUM SPIN CHAINS [J].

FANNES, M ;

NACHTERGAELE, B ;

WERNER, RF .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 144 (03) :443-490

[5] HIGH-TEMPERATURE SERIES EXPANSIONS FOR THE (2 + 1)-DIMENSIONAL ISING-MODEL [J].

HE, HX ;

HAMER, CJ ;

OITMAA, J .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (10) :1775-1787

[6] Vertical density matrix algorithm: A higher-dimensional numerical renormalization scheme based on the tensor product state ansatz [J].

Maeshima, N ;

Hieida, Y ;

Akutsu, Y ;

Nishino, T ;

Okunishi, K .

PHYSICAL REVIEW E, 2001, 64 (01) :6-016705

[7] Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states [J].

Murg, V. ;

Verstraete, F. ;

Cirac, J. I. .

PHYSICAL REVIEW A, 2007, 75 (03)

[8]

Nishio Y., ARXIVCONDMAT0401115

[9]

OITMA J, 2006, SERIES EXPANSION MET

[10] LOW-TEMPERATURE SERIES EXPANSIONS FOR THE (2+1)-DIMENSIONAL ISING-MODEL [J].

OITMAA, J ;

HAMER, CJ ;

WEIHONG, Z .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (12) :2863-2867

← 1 2 3 →