Quantum transverse-field Ising model on an infinite tree from matrix product states

被引：45

作者：

Nagaj, Daniel ^{[1
]}

Farhi, Edward ^{[1
]}

Goldstone, Jeffrey ^{[1
]}

Shor, Peter ^{[1
]}

Sylvester, Igor ^{[1
]}

机构：

[1] MIT, Ctr Theoret Phys, Cambridge, MA 02139 USA

来源：

PHYSICAL REVIEW B | 2008年 / 77卷 / 21期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevB.77.214431

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We give a generalization to an infinite tree geometry of Vidal's infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

引用

页数：15

共 19 条

[1]

Baxter R. J., 1982, EXACTLY SOLVED MODEL, P47

[2] Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces -: art. no. P04005 [J].