Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Theoretical Physics

Quantum Phase Transitions in Conventional Matrix Product Systems

Jing-Min Zhu, Fei Huang, Yan Chang

Published Nov 2, 2016• 0 citations
Publisher
DOI
10.1007/s10773-016-3163-z

Related papers

Bell-CHSH function approach to quantum phase transitions in matrix product systems

Hailin Huang, Zhao‐Yu Sun, Bo Wang

arXiv:1304.3759•The European Physical Journal B•Jun 1, 2013•11 citations

Quantum Phase Transitions in Matrix Product Systems

Michael M. Wolf, Gerardo Ortíz, Frank Verstraete +1 more

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of "conventional" QPTs.

arXiv:cond-mat/0512180•Physical Review Letters•Sep 12, 2006•151 citations

Quantum phase transitions and bifurcations: reduced fidelity as a phase transition indicator for quantum lattice many-body systems

Jinhua Liu, Qian‐Qian Shi, Jian-Hui Zhao +1 more

We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking order. Our finding is based on the observation that in the conventional Landau–Ginzburg–Wilson paradigm a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking that is captured by a local-order parameter, which in turn results in an essential change of the reduced density matrix in the symmetry-broken phase. Two quantum systems on an infinite lattice in one spatial dimension, i.e. a quantum Ising model in a transverse magnetic field and a quantum spin-1/2 XYX model in an external magnetic field, are considered in the context of the tensor network algorithm based on the matrix product state representation.

arXiv:0905.3031•Journal of Physics A Mathematical and Theoretical•Nov 17, 2011•6 citations

Quantum phase transitions in low dimensional systems

Kazuo Ueda, 上田 和夫

•Jan 1, 2000•0 citations

Phase Transitions in Quantum Systems

WORLD SCIENTIFIC eBooks•Nov 1, 2013•0 citations

Path selection rule in matrix product systems

Zhao‐Yu Sun, K.L. Yao, Bo Luo +3 more

A matrix product system chooses a special path in the phase diagram to undergo a quantum phase transition (QPT) and shows different behaviors compared with a traditional QPT, such as the symmetry behavior of some physical observables described in this paper. An equation is established, which (i) helps one to understand the special behaviors of a matrix product state (MPS)-QPTs, and (ii) can be used to detect the QPT point of a MPS, much simpler than usual procedures of calculating the transfer matrix or density matrix of the system. The equation acts as a selection rule for the path of the MPS-QPT and is believed to be the essence of distinguishing a MPS-QPT from a traditional QPT. Furthermore, the discontinuity of the derivative of an observable is found to be connected directly to the turning point in the path of the MPS, but not the phase boundary point in the phase diagram, though the two are in accordance with each other in many cases.

Physical Review B•Sep 22, 2009•1 citation
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of "conventional" QPTs.
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking order. Our finding is based on the observation that in the conventional Landau–Ginzburg–Wilson paradigm a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking that is captured by a local-order parameter, which in turn results in an essential change of the reduced density matrix in the symmetry-broken phase. Two quantum systems on an infinite lattice in one spatial dimension, i.e. a quantum Ising model in a transverse magnetic field and a quantum spin-1/2 XYX model in an external magnetic field, are considered in the context of the tensor network algorithm based on the matrix product state representation.
A matrix product system chooses a special path in the phase diagram to undergo a quantum phase transition (QPT) and shows different behaviors compared with a traditional QPT, such as the symmetry behavior of some physical observables described in this paper. An equation is established, which (i) helps one to understand the special behaviors of a matrix product state (MPS)-QPTs, and (ii) can be used to detect the QPT point of a MPS, much simpler than usual procedures of calculating the transfer matrix or density matrix of the system. The equation acts as a selection rule for the path of the MPS-QPT and is believed to be the essence of distinguishing a MPS-QPT from a traditional QPT. Furthermore, the discontinuity of the derivative of an observable is found to be connected directly to the turning point in the path of the MPS, but not the phase boundary point in the phase diagram, though the two are in accordance with each other in many cases.