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

Chinese Physics C

Quantum phase transitions in matrix product states of one-dimensional spin-½ chains

Jing-Min Zhu

Published Dec 1, 2014• 0 citations
Publisher

Abstract

For the matrix product system of a one-dimensional spin-½ chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψ a 〉 = |1...1〉 representing all particles spin up and |Ψ b 〉 = |0...0〉 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N -qubit maximally entangled GHZ state . At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -qubit maximal entanglement.

DOI
10.1088/1674-1137/38/12/123102

Related papers

Quantum phase transitions in matrix product states of one-dimensional spin-1/2 chains

祝敬敏

For the matrix product system of a one-dimensional spin-1/2chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa =|1··· 1> representing all particles spin up and |Ψb =|0··· 0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state |Ψpt =21/2/2(|1··· 1> +|0··· 0>). At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

Chinese Physics C•Jan 1, 2014•0 citations

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

Jing-Min Zhu

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.

Chinese Physics C•Oct 1, 2014•1 citation

Quantum phase transitions in composite matrix product states of one-dimensional spin-1/2 chains

Jing-Min Zhu

For matrix product states of one-dimensional spin-1/2 chains, we investigate the properties of quantum phase transition of the proposed composite system. We find that the system has three different ferromagnetic phases, one line of the two ferromagnetic phases coexisting equally describes the paramagnetic state, and the other two lines of two ferromagnetic phases coexisting equally describe the ferrimagnetic states, while the three phases coexisting equally point describes the ferromagnetic state. Whether on phase transition lines or at the phase transition point, the system is always in an isolated mediate-coupling state, the physical quantities are discontinuous and the system has long-range correlation and has long-range classical correlation and long-range quantum correlation. We believe that our work is helpful for comprehensively and profoundly understanding the quantum phase transitions, and of some certain guidance and enlightening on the classification and measure of quantum correlation of quantum many-body systems.

International Journal of Modern Physics B•Feb 16, 2015•5 citations

Entanglement and quantum phase transitions in matrix-product spin-1 chains

S. Alipour, Vahid Karimipour, Laleh Memarzadeh

We consider a one-parameter family of matrix-product states of spin-1 particles on a periodic chain and study in detail the entanglement properties of such a state. In particular, we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other, and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point the character of the matrix-product state, which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that the entanglement of two sites have scaling behavior near the critical point.

arXiv:quant-ph/0702036•Physical Review A•May 17, 2007•25 citations

Quantum Phase Transitions in Matrix Product States

Jing-Min Zhu

We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.

Chinese Physics Letters•Oct 1, 2008•10 citations

Quantum phase transitions about parity breaking in matrix product systems

Jing-Min Zhu

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.

Chinese Physics C•Feb 1, 2011•6 citations
For the matrix product system of a one-dimensional spin-½ chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψ a 〉 = |1...1〉 representing all particles spin up and |Ψ b 〉 = |0...0〉 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N -qubit maximally entangled GHZ state . At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -qubit maximal entanglement.
For the matrix product system of a one-dimensional spin-1/2chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa =|1··· 1> representing all particles spin up and |Ψb =|0··· 0> representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state |Ψpt =21/2/2(|1··· 1> +|0··· 0>). At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.
We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.
For matrix product states of one-dimensional spin-1/2 chains, we investigate the properties of quantum phase transition of the proposed composite system. We find that the system has three different ferromagnetic phases, one line of the two ferromagnetic phases coexisting equally describes the paramagnetic state, and the other two lines of two ferromagnetic phases coexisting equally describe the ferrimagnetic states, while the three phases coexisting equally point describes the ferromagnetic state. Whether on phase transition lines or at the phase transition point, the system is always in an isolated mediate-coupling state, the physical quantities are discontinuous and the system has long-range correlation and has long-range classical correlation and long-range quantum correlation. We believe that our work is helpful for comprehensively and profoundly understanding the quantum phase transitions, and of some certain guidance and enlightening on the classification and measure of quantum correlation of quantum many-body systems.
We consider a one-parameter family of matrix-product states of spin-1 particles on a periodic chain and study in detail the entanglement properties of such a state. In particular, we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other, and show that the derivative of both these properties diverge when the parameter ggg of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point the character of the matrix-product state, which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that the entanglement of two sites have scaling behavior near the critical point.
We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.
According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.