Unfrustrated qudit chains and their ground states

被引：22

作者：

Movassagh, Ramis ^{[1
]}

Farhi, Edward ^{[2
]}

Goldstone, Jeffrey ^{[2
]}

Nagaj, Daniel ^{[3
]}

Osborne, Tobias J. ^{[4
]}

Shor, Peter W. ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

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

[3] Slovak Acad Sci, Inst Phys, Res Ctr Quantum Informat, Bratislava, Slovakia

[4] Wissensch Skolleg Berlin, Inst Adv Study, Berlin, Germany

来源：

PHYSICAL REVIEW A | 2010年 / 82卷 / 01期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevA.82.012318

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We investigate chains of d-dimensional quantum spins (qudits) on a line with generic nearest-neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, that is, when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the matrix product states (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.

引用

页数：5

共 50 条

[1] Ground states of unfrustrated spin Hamiltonians satisfy an area law
de Beaudrap, Niel
Osborne, Tobias J.
Eisert, Jens
NEW JOURNAL OF PHYSICS, 2010, 12
[2] Qudit hypergraph states
Steinhoff, F. E. S.
Ritz, C.
Miklin, N. I.
Guehne, O.
PHYSICAL REVIEW A, 2017, 95 (05)
[3] Exact ground states for interacting Kitaev chains
Wouters, Jurriaan
Katsura, Hosho
Schuricht, Dirk
PHYSICAL REVIEW B, 2018, 98 (15)
[4] Alternating spin chains with singlet ground states
Fukui, T
Kawakami, N
PHYSICAL REVIEW B, 1997, 56 (14) : 8799 - 8806
[5] Ground states for nonuniform periodic Ising chains
Martinez-Garcilazo, J. P.
Ramirez, C.
PHYSICAL REVIEW E, 2015, 91 (04):
[6] Qudit hypergraph states and their properties
Xiong, Fei-Lei
Zhen, Yi-Zheng
Cao, Wen-Fei
Chen, Kai
Chen, Zeng-Bing
PHYSICAL REVIEW A, 2018, 97 (01)
[7] Exact ground states for polyphenylene type of hexagon chains
Trencsenyi, Reka
Gulacsi, Katalin
Kovacs, Endre
Gulacsi, Zsolt
ANNALEN DER PHYSIK, 2011, 523 (8-9) : 741 - 750
[8] EXACT GROUND STATES OF CORRELATED ELECTRONS ON PENTAGON CHAINS
Gulacsi, Zsolt
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2013, 27 (14):
[9] Exact ground states of spin-2 chains
Ahrens, MA
Schadschneider, A
Zittartz, J
EUROPHYSICS LETTERS, 2002, 59 (06): : 889 - 895
[10] Multipartite entanglement in qudit hypergraph states
Malpetti, D.
Bellisario, A.
Macchiavello, C.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2022, 55 (41)

← 1 2 3 4 5 →